Calculator – Page 3

Implicit Differentiation Calculator | Calculate Implicit Differentiation

April 23, 2021April 7, 2021 by Veerendra

Enter your equation and data items in the input box and click on the calculate button to obtain the Implicit Differentiation for your equation. Use this handy free online Implicit Differentiation Calculator tool to get the accurate output of an equation in a fraction of seconds.

Implicit Differentiation Calculator: If you want to calculate implicit differentiation of an equation use this handy calculator tool. It is not easy for anyone to find the implicit differentiation at the given point. So, to assist you in this we are giving the lengthy manual step by step process to solve the implicit differentiation of the equation. Here, we are also giving an example for your better understanding.

Steps to Solve Implicit Differentiation of Equation

The simple and easy procedure to find the implicit differentiation of the equation is mentioned below. Go through the step by step process and follow them while solving the equation.

Let us take any polynomial equation contains two variables x and y
Apply the differential function on the both sides of the equation i.e dy/dx
Calculate the derivatives
Bring dy/dx on the one side of the equation
Do the mathematical operations to the dy/dx value
Substitute given (x,y) values in the obtained expression
The obtained number is your answer.

Example

Solve Implicit Differentiation of x³+y³=2xy at (x,y)=(2,3)?

Solution:

Given equation is

x³+y³=2xy

Derivative of the equation is

dy/dx(x³)+dy/dx(y³)=dy/dx(2xy)

3x²+3y²dy/dx=2xdy/dx+2y

3y²dy/dx-2xdy/dx=2y-3x²

dy/dx(3y^2-2x)=2y-3x^2

dy/dx=2y-3x²/3y²-2x

dy/dx at (2,3) is substitute x=2 and y=3 in the above equation

=2(3)-3(2)²/3(3)²-2(2)

=6-12/27-4

=-6/23

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FAQs on Implicit Differentiation Calculator

1. Why do we use implicit differentiation?

Implicit differentiation technique allows you to find out the derivative of y with respect to x without having to solve the general equation for y.

2. What is the implicit differentiation of xy?

The implicit differentiation of xy is

dy/dx(xy)=xy’+x’y

=xy’+y

3. What are the differences between implicit differentiation and partial differentiation?

In implicit differentiation, all the variables are differentiated. In partial differentiation, the derivative is done only one variable by leaving other variables as constants.

4. What is meant by implicit function?

Implicit function is a function where dependent and independent variables are kept on one side of the equation.

Triple Integral Calculator | Solve Triple Integral Function

April 23, 2021April 7, 2021 by Veerendra

Free handy Triple Integral Calculator is here to calculate the triple integral of a function within a short span of time. Just provide the input function and bounds in the input section of the calculator and press on the calculate button to get the result immediately.

Triple Integral Calculator: If you are struggling to figure out the triple integral of a function you have come the right way. Take the help of our free Triple Integral Calculator tool to get the instant output for your expression. Along with this calculator, you can also learn the step by step procedure to solve the triple integral function easily. For your better understanding we have also provided an example question in the below sections.

Steps to Solve Triple Integral Function

Triple integral is similar to double integral. In triple integral, you need to calculate the integration for three different variables with respect to three variables. Check the following module to get an idea on how to solve the triple integral. Follow these guidelines and compute the function simply.

Take any function have three variables to solve the triple integral
First you need to perform the integration with respect to one variable to eliminate that variable.
After integration substitute the bound values in the expression i,e upper limit – lower limit
Important point is while performing integration with respect to one variable, you need to consider the other two variables as constants.
After eliminating the first variable, you have to repeat the process in the same way to eliminate the remaining variable and get your answer in constant.

Example

Question: Solve ∫₀³∫₂³ ∫₁² x²y²z² dxdydz?

Solution:

Given that

∫₀³ ∫₂³ ∫₁² x²y²z² dxdydz

At first, perform integration with respect to x

∫₀³ ∫₂³ x³/3*3y²z² dydz

Substitute the limit values in obtained expression

∫₀³ ∫₂³ y²z² dydz [2³-1³/3]

=∫₀³ ∫₂³ y²z² dydz [8-1/3]

=∫₀³ ∫₂³ y²z² dydz [7/3]

Calculate integration with respect to y

=∫₀³ y³/3*7z²/3 dz

=∫₀³ 7z²/3 dz [3³-2³/3]

=∫₀³ 7z²/3 dz [27-8/3]

=∫₀³ 7z²/3 dz [19/3]

=∫₀³ 133z²/9 dz

Now, perform integration with respect to z

=133/9 * z³/3

Replacing the bound values

=133/9 * [3³-0³/3]

=133/9 * 27/3

=133

∫₀³∫₂³ ∫₁² x²y²z² dxdydz= 133

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FAQs on Triple Integral Calculator

1. Where we can use triple integrals?

Triple integrals are the analog of double integrals for three dimensionals. They are used to find the volume of a three dimensional space and for adding up infinity quantities associated with points in a three dimensional region.

2. Is triple integral volume?

Triple integrals are used to find volume, just like double integrals are used to find mass, when volume of the region has variable density.

3. How do you find the volume of a triple integral?

The volume of an ellipsoid is expressed using the triple integral which is V=∭U dxdydz=∭U′abcρ2sinθdρdφdθ. By symmetry, you can find the volume of ellipsoid lying in the first octant (x≥0, y≥0, z≥0) and multiply the result by 8.

4. How to compute Triple Integrals?

Solving triple integrals is the same as double integrals. Here, you need to solve the integration of three variables in the given range. Solve the integration and substitute the range value in the obtained expression to get the answer.

Maclaurin Series Calculator | Maclaurin Series of Function

April 23, 2021April 6, 2021 by Veerendra

We are pretty sure you can easily find the Maclaurin Series of a function easily using our free Maclaurin Series Calculator tool. Just enter your input function and range values in the specified input fields and hit the calculate button to check the Maclaurin series of function in a fraction of seconds.

Maclaurin Series Calculator: Do you feel solving Maclaurin Series of function is difficult? Then you are on the right place. You can get the step by step procedure to solve the maclaurin series function in a shot span of time. This Maclaurin Series Calculator gives the answer for your question immediately. Go through the following sections to get a clarity on the Maclaurin Series.

Steps to Compute Maclaurin Series of Function

Below mentioned are the simple and easy steps that are helpful while solving the maclaurin series function. Follow these guidelines

Take any function and its range to solve the Maclaurin Series.
For any function f(x) the maclaurin series is given by f(x)=∑_k=0^∞ f^(k) (a)* x^k/ k!
Find f^(k) (a) by calculating the function derivative and substituting the range values in the function.
Compute the k! for each step.
Replace the values in the above formula.
Apply sigma function and obtain the answer.

Example

Question: Calculate Maclaurin Series of sin(x) up to n = 5?

Solution:

Given function f(x)= Sin(x)

n = 0 to 5

Maclaurin series for the function is f(x)=∑_k=0^∞ f^(k) (a)* x^k/ k!

f(x)≈ ∑_k=0⁵ f^(k) (a)* x^k/ k!

So, calculate the derivative and evaluate them at the given point to get the result into the given formula.

f⁰(x) = f(x) = sin(x)

Evaluate function: f(0) = 0

Calculate first derivative f¹(x) = [f⁰(x)]’

= [sin(x)]’ = cos(x)

[f⁰(x)]’ = cos(x)

Evaluate first derivative (f(0))’ = cos(0) = 1

Second Derivative: f²(x) = [f¹(x)]’ = [cos(x)]’ = -sin(x)

(f(0))′′=0

Third derivative: f³(x) = [f²(x)]’ = (-sin(x))’ = -cos(x)

Evaluate third derivative (f(0))”’ = -cos(0)

= -1

Fourth derivative: f⁴(x) = [f³(x)]’ = [-cos(x)]’ = sin(x)

Evaluate 4th derivative (f(0))”” = sin(0) = 0

Fifth derivative: f⁵(x) = [f⁴(x)]’ = [sin(x)]’ = cos(x)

Evaluate 5th derivative (f(0)””’ = cos(0) = 1

Replace the derivative values in the above formula

f(x) ≈ 0/0! x⁰ + 1/1! x¹ + 0/2! x² + (-1)/3! x³ + 0/4! x⁴ + 1/5! x⁵

f(x) ≈ 0 + x + 0 – 1/6 x³ + 0 + 1/120 x⁵

sin(x) ≈ x-1/6 x³ + 1/120 x⁵

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Frequently Asked Questions on Maclaurin Series

1. How do you define the Maclaurin Series?

Maclaurin Series is defined as the expanded series of the function. Here, approximate value of the function can be evaluated as the sum of derivatives of the function.

2. What is the difference between Maclaurin and Taylor Series?

Taylor Series is the representation of a function as an infinite sum of terms calculated from the values of its derivatives at a single point. Maclaurin series is a special case of tayloe series which uses zero as a single point.

3. How does Maclaurin series work?

A maclaurin series is a power series that allows you to calculate an approximation of function f(x) for the input values close to zero, given that one knows the values of the successive derivatives of the function at zero.

4. What is the formula of Maclaurin series?

Maclaurin series for function is defined as f(x)=∑_k=0^∞ f^(k) (a)* x^k/ k!

Indefinite Integral Calculator

April 23, 2021April 6, 2021 by Veerendra

Indefinite Integral Calculator directly gives the integral of your input function easily in fraction of seconds. Just enter function as the input in the specified fields and tap on the calculate button which is available next to the input section to find the result in seconds.

Indefinite Integral Calculator: Do you feel calculating indefinite integral somewhat difficult? Not anymore with the help of our easy to use online calculator tool. Now, you can solve the integration of any function easily and instantly by using our Indefinite Integral Calculator. Refer the below section, to get familiar with this concept by checking the solved examples. The step by step process to compute the indefinite integral is also mentioned here.

Procedure to Find Indefinite Integral of Function

Indefinite integral is an integral without having upper and lower limits. The step by step process of evaluating indefinite integrals is listed here. So, follow the steps given here and do calculations easily by hand.

Take any function to compute the indefinite integral.
Go through the different rules like power rule, exponential, constant rule, etc before solving the problem.
∫ x dx is always equal to (x²) / 2 + C. Where C is the constant
Integration of any constant is equal to the constant value * x + C.
If the function is in the difficult form.
Consider one part of the function as a variable and substitute that variable in all the possible places of the fumction.
Find integration with respect to that variable and substitute the value.

Examples

Question 1: Solve ∫ (2x + 1 ) / (x+5)³ dx?

Solution:

Given input Mixed Number is 2 4/3

∫ (2x + 1 ) / (x+5)³ dx

Let us take,

u = x + 5

Then, 2x + 1 = 2u – 9

∫ (2x + 1 ) / (x+5)³ dx = ∫ (2u – 9) / u³ du

= ∫ 2u / u³ – 9/ u³ du

= ∫ 2/u² – 9/u³ du

Apply the sum rule ∫ f(x) + g(x) dx = ∫ f(x) dx + ∫ g(x) dx

= ∫ 2/u² du – ∫ 9/u³ du

Take out the constant: ∫ a. f(x) dx = a. ∫ f(x) dx

= 2 ∫ 1/ u² du – 9 ∫ 1 / u³ du

Apply exponent rule 1/ a^b = a^-b

= 2 ∫ u^-2 du – 9 ∫ u^-3 du

Apply the Power rule: ∫ x^a dx = x^a+1 / a+1, a ≠ 1

= 2 * u^-2+1 / (-2+1) – 9 * u^-3+1 / (-3+1)

= 2 * u^-1 / (-1) – 9 * u^-2 / (-2)

= -2/u + 9/2u²

Substitute u = x + 5 in the above

= -2/(x + 5) + 9/2( x + 5)²

∫ (2x + 1 ) / (x+5)³ dx = -2/(x + 5) + 9/2( x + 5)² + C

Question 2: Solve ∫ (x² + 3x – 2) dx?

Solution:

∫ (x² + 3x – 2) dx

= ∫ x² dx + ∫ 3x dx – ∫ 2 dx

= x³/3 + (3x)² / 2 – 2x + C

= x³/3 + 9x²/2 – 2x + C

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FAQs on Indefinite Integral Calculator

1. What is Meant by Indefinite Integrals?

Indefinite Integral is an integration function indicated without lower and upper limits and with an arbitrary constant C. It is considered as an easy way to symbolize the antiderivative of the function. The representation is ∫ f (x) dx. The function f(x) is called Integrand.

2. Why we add a constant with an Indefinite Integral?

Integral function is called its anti derivative. If you differentiate a function and then integrate it, you should get the function back.

For example take f(x) = x, g(x) = x + 4

f′(x)=1 and g'(x) = 1.

If you not add constant

∫f′(x) dx = x, ∫g'(x) dx = x

Here, you are not getting exact g(x) value. So, we are adding constant.

∫f′(x) dx = x + C1, ∫g'(x) dx = x + C2

C1 = 0, C2 = 4.

3. What are the rules of Integration?

Integration is used to find area, volume, etc. The some of the common rules of integration are:

1. Constant rule: ∫a dx = ax + C

2. Multiplication by constant: ∫cf(x) dx = c ∫f(x) dx

3. Reciprocal rule: ∫(1/x) dx = log(x) + C

4. Exponential rules: ∫ex dx = ex + C, ∫ax dx = ax/log(a) + C, ∫log(x) dx = x log(x) − x + C.

4. Can an Integral have 2 Answers?

No, integrals don’t have two answers. Let us say, x+c, x²+c both cannot be solutions to same integral, because x and x² don’t differ by constant.

Integration By Parts Calculator | Free Handy Calculator

April 23, 2021April 6, 2021 by Veerendra

Use online and handy Integration By Parts Calculator to get the exact answer after integrating your function. All you have to do is provide the input expression and click on the calculate button to display the related output in no time.

Integration By Parts Calculator: Want to calculate the integration by parts of an expression in an easy way? Then you must go through the below sections of this page. Here, we are offering the simple and easy method to solve the integration of an expression by parts.

This page is all about calculating integration of an expression using Integration by Parts Calculator and the interactive tutorial explains each and every step of the process. This free calculator is easy to use because it is having the flexible user interface which helps to explore more about the concepts.

How to Calculate Integration By Parts of an Expression?

In mathematics, integration by parts is a special method of integration when two functions are multiplied. The following are the steps that help you in solving the different integrals. Follow them to do the integration of an expression manually

Take any function in the form of ∫u v dx. Where u and v are the two different functions
The formula to calculate these types of functions using integration by parts method is ∫u⋅dv=u⋅v−∫v⋅du
Identify u and v functions in your expression and substitute them in the formula
First calculate Integration of dv to obtain v
Then, calculate integration v with respect to v.
Replace the obtained values in the formula to get the solution.

Example

Question: Solve ∫x. cos(x) dx by using integration by parts method?

Solution:

Given that,

∫x. cos(x) dx

The formula of integration by parts is ∫u⋅dv=u⋅v−∫v⋅du

So, u=x

du=dx

dv=cos(x)

∫cos(x) dx= sin(x)

By substituting the values in the formula

∫x. cos(x) dx= x.sin(x)-∫sin(x) dx

=x.sin(x)+cos(x)

Therefore ∫x. cos(x) dx=x.sin(x)+cos(x)+C

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FAQs on Integration By Parts Calculator

1. How is the product rule related to integration by parts?

From the product rule, we can get the integration by parts formula. It is used when integrating the product of two expressions.

2. How do you calculate integration by parts?

The formula to calculate integration of any product expression by using integration by parts method is ∫u⋅dv=u⋅v−∫v⋅du. The formula replaces one integral with another. It means the one on the right is simpler to evaluate.

3. What is the goal of integration by parts?

The main goal of integration by parts method is to replace a difficult integral with one that is easier to evaluate.

4. Compute ∫ x lnx dx by using integration by parts process?

Integration by parts formula is ∫u⋅dv=u⋅v−∫v⋅du

From that u=x, du=dx

dv=logx, ∫ logx dx=x(log(x)-1)+C

∫ logx dx= xlog(x)-x+C

∫ x lnx dx= (½)x2 log x – (x2/4) + C

Partial Derivative Calculator | Free Online Math Calculator

April 23, 2021April 6, 2021 by Veerendra

Looking for a tool that does Partial Derivation easily? Utilize our Partial Derivative Calculator tool and obtain the result instantly. Provide input function in the input fields and click on the calculate button to get the partial derivative of the given function along with the detailed solution.

Partial Derivative Calculator: Are you scared of finding the partial derivatives? To help you in this we have given the free Partial Derivative Calculator that does all your derivative calculations in fraction of seconds. We have included the step by step procedure on how to solve the partial differential equation. You can use this online calculator tool to verify whether your answers are accurate or not after performing partial derivative function.

How to Find Partial Derivative of Function?

Partial Derivative is nothing but the derivative of a function of multiple variables with respect to one variable and all other variables are kept constant. No need to get panic to solve the partial derivative of an expression. You can simply go through the following mentioned steps and use them to get the partial derivative easily.

Take any function to compute the partial derivative
You must know the derivative of sum/ difference is the sum/ difference of derivatives and the derivative of a constant is zero.
When you apply a derivative with respect to one variable, solve the derivation with respect to that particular variable only.
Solve all the derivative functions and the result will be your answer.

Example

Question: Solve ∂²/∂x [4x²y³+x²] using partial differentiation method?

Solution:

Given that,

∂²/∂x [4x²y³+x²]= ∂/∂x[∂/∂x(4x²y³+x²)

Let us take function f=4x²y³+x²

∂f/∂x= 8xy³+2x

We can also write ∂²/∂x [4x²y³+x²] = ∂/∂x(∂f/∂x)

=∂/∂x (8xy³+2x)

Consider y as constant

=8y³+2

∂²/∂x [4x²y³+x² = 8y³+2 = 2(4y³+1)

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FAQs on Partial Derivative Calculator

1. What is the difference between a derivative and a partial derivative?

Derivative isa applied to a function that has only one independent variable. Partial derivative is applied to functions that have more than one independent variable.

2. Why are partial derivatives used?

Partial differentiation is used to differentiate mathematical functions having more than one variable in them.

3. Can you integrate a partial derivative?

Yes, we can integrate the function f(x,y) with respect to x, a process refer as partial integration. Suppose for the function f(x,y) do the partial derivative with respect to y and integrate f(x,y) with respect to y.

4. Does order of partial derivatives matter?

The order of partial differentiation does not matter for any function. We may first differentiate with respect to one variable and then with respect to another.

Double Integral Calculator | Free Online Calculator

April 23, 2021April 6, 2021 by Veerendra

Our free handy Double Integral Calculator tool is aimed at giving the double integral of a function within fraction of seconds. The only one thing you need to do is just give your function and range for two variables as input and obtain the value as output immediately after hitting the calculate button.

Double Integral Calculator: Finding the definite integral for a function is similar as double integral. But in case of double integral, you need to perform the same operation twice. It is a bit difficult for anyone to get the double integral of an expression. So, we advise you to use this online Double Integral Calculator to generate your answer instany. Checkout the further sections of this article to know the detailed process with an example.

How to Compute Double Integral of a function?

People can go through the below sections to get the complete procedure to find the double integral. Follow these steps to get the answer for your function.

Let us take any function with x and y values
To compute the double integral of that function f(x), first perform the integration for with respect to y
After that, substitute the x range values (a,b) in function to obtain f(b) and f(a)
Calculate f(b)-f(a)
Again perform integration with respect to other variable
Repeat Step 3 and Step 4 to get the result

Example

Question: Compute ∫₀¹(∫₀²xy^2dx).dy?

Answer:

Given function

f(x)=xy^2

∫xy^2=x^2y^2/2

f(0)=(0)^2y^2/2=0

f(2)=(2)^2y^2/2=2y^2

∫₀²xy^2dx=f(2)-f(0)

=2y^2

∫₀¹(∫₀²xy^2dx).dy=∫₀¹2y^2dy

∫2y^2dy=2y^3/3

f(0)=2(0)^3/3

f(1)=2(1)^3/3=⅔

∫₀¹(∫₀²xy^2dx).dy=f(1)-f(0)

=⅔-0

=2/3

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Frequently Asked Questions on Double Integral Calculator

1. What is the application of double integral?

Double integrals are mainly used to calculate the area of a region in the graph, the volume of surface, and the average value of a function of two variables over a rectangular region.

2. Does order matter in double integral?

In some cases, the order of integral is not a matter. You can change the order of integration. But you need to rewrite the iterated integral.

3. How do you solve the double integral of a function?

To calculate double integral of any function, you need to compute integral with respect to y, this removes x variable. Then, calculate integral with respect to y.

4. Can you split double integral?

According to Fubini’s theorem, we can split up double integrals into iterated integrals.

5. What is the integral used for?

Generally, integrals are used for calculating the area of a two dimensional region, and volume of a 3 dimensional object that is having curved boundary.

Best Taylor Series Calculator | Free Online Calculator Tool

April 23, 2021April 6, 2021 by Veerendra

By using free Taylor Series Calculator, you can easily find the approximate value of the integration function. Just provide the function, expansion order and expansion variable in the specified input fields and press on the calculate button to check the result of integration function immediately.

Taylor Series Calculator: If you are searching for a best tool that finds the integration function value using Taylor Series, then you are at the correct place. You will get the handy Taylor Series Calculator tool that provides you the answer within no time. Along with the exact result, you will also find the lengthy explanation to solve a function using Taylor Series. Below provided step by step procedure is helpful for you in solving the function easily.

Steps to Solve Integration of Function using Taylor Series

Follow these simple steps to solve any function integration using taylor series. These steps are useful for you to get a clear idea on the concept.

Let us consider any function to find the integration, upper and lower limits of integration.
Taylor Series formula for a function f is f(x) = f(a) + f'(a)(x-a) + f”(a)/2 (x-a)² + f”'(a)/3! (x-a)³ + . . . + f⁽ⁿ⁾(a)/n! (x-a)ⁿ
Where, a is the centre.
First of all find the derivative of given function and evaluate the derivative at the given point.
Substitute the obtained values in the above formula to get a polynomial.
Finally, simplify your polynomial expression to get the final answer.

Example

Question: Calculate Taylor Series of sin(x) up to n=5, centre is 1?

Solution:

Given function is f(x) = sin(x)

n = 0 to 5, centre = 1

Taylor Series formula is f(x) = f(a) + f¹(a)(x-a) + f²(a)/2 (x-a)² + f³(a)/3! (x-a)³ + . . . + f⁽ⁿ⁾(a)/n! (x-a)ⁿ

By using the above values f(x) will become

f(x) = f(0) + f¹(1)(x-1) + f²(2)/2 (x-2)² + f³(3)/3! (x-1)³ + f⁴(4)/4! (x-1)⁴ + f⁵(5)/5! (x-1)⁵

So, calculate the derivative and evaluate them at the given point to get the result into the given formula.

f⁰(x) = f(x) = sin(x)

f(0) = sin(0) = 0

First derivative of f(x) is f¹(x) = [f⁰(x)]’

= [sin(x)]’

= cos(x)

[f(0)]’ = cos(0) = 1

Second Derivative: f²(x) = [f¹(x)]’ = [cos(x)]’ = -sin(x)

(f(0))′′= 0

Evaluate third derivative (f(0))”’ = -cos(0) = -1

Fourth derivative f⁴(x) = [f³(x)]’ = [-cos(x)]’ = sin(x)

(f(0))”” = sin(0) = 0

Fifth derivative: f⁵(x) = [f⁴(x)]’ = [sin(x)]’ = cos(x)

(f(0))””’ = cos(0) = 1

Substitute these values in the taylor formula

f(x) ≈ 0 + 1 (x-1) + 0/2 (x-2)² + (-1)/6 (x-1)³ + 0/4! (x-1)⁴ + 1/5! (x-1)⁵

≈ (x-1) – 1/6 (x-1)³ + 1/120 (x-1)⁵

sin(x) ≈ (x-1) – 1/6 (x-1)³ + 1/120 (x-1)⁵

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FAQs on Taylor Series Calculator

1. How do you use Taylor Series Calculator to solve the functions?

The step by step process to use this calculator is provided here. Enter the function, limit and center in the respective input fields. Hit on the calculate button to get the series in the output window.

2. Solve x²+2x with centre 3 using taylor series?

Given fuunction is x²+2x

Taylor Series formula is f(x) = f(a) + f'(a)(x-a) + f”(a)/2 (x-a)² + f”'(a)/6 (x-a)³

f(3) = (3)²+2(3) = 15

f'(x) = 2x+2

f'(3) = 6+2=8

f”(x) = 2

f”'(x) = 0

Replace the obtained values in the formula

f(x) = 15+ 8(x-3) + 2(x-3)² + 0(x-3)³

x²+2x = 15 + 8(x-3) + 2(x-3)²

3. What is meant by Taylor Series?

Taylor Series is defined as the expression of the function as the infinite series, in which the terms are expressed for the value of functions derivative at a single point. It is used to draw the conclusion of what a function looks like.

4. What is Taylor series method?

Taylor series method is one of the earliest analytic numeric algorithms to find approximate solution of initial value problems for ordinary differential equations.

Derivative Calculator | Steps to find Derivative of function

April 23, 2021April 6, 2021 by Veerendra

Free Derivative Calculator helps you to find the differentiation of the given function, with steps shown. Make your calculations easier and faster by giving the input function and tap on the calculate button to get the output as derivative of the function in no time.

Derivative Calculator: Struggling to calculate the derivative of a function? Then, here is the solution for your problem. Differentiation can be calculated easily by using the differentiation rules. You can understand and learn about the entire concept from here and also get the simple steps to solve the questions. Our handy calculator does all the required calculations and displays the exact output along with all the steps of calculations in fraction of seconds.

Here are the easy steps that should be followed while finding the derivative. The steps are along the lines:

Take any function to calculate the derivative.
Have a look at the basic formulas or rules that are useful to solve the differentiation.
Apply those rules and solve the function easily.

Important Derivative Rules

Below mentioned are the some important derivate rules that are used while solving the derivative of any function. Have a look at them.

d/dx (a) = 0 (where a is a constant)
d/dx (x) = 1
d/dx (xⁿ) = nx^n-1 [power rule]
d/dx (e^x) = e^x [exponent rule]
d/dx (log x) = 1/x
d/dx (a^x) = a^x logx
d/dx (f+g) = d/dx (f) + d/dx (g)
d/dx (f-g) = d/dx (f) – d/dx (g)
d/dx (ay) = a dy/dx
(f.g)’ = f’g + g’f [product rule]
(f/g)’ = (f’g – g’f) / (g²) [quotient rule]
d/dx (f(g(x) = f'(g(x))g'(x) [chain rule]
For Trigonometric Functions:
- d/dx sin(x) = cos(x)
- d/dx cos(x) = -sin(x)
- d/dx tan(x) = sec²(x)
- d/dx cot(x) = -cosec²(x)

Example

Question: Solve derivative of 6 / √z³ + 1 / (8z⁴) – 1 / (3z¹⁰)

Solution:

Given function is 6 / √z³ + 1 / (8z⁴) – 1 / (3z¹⁰)

d/ dz ( 6 / √z³ + 1 / (8z⁴) – 1 / (3z¹⁰)) = ?

= d/ dz ( 6 z^-3/2 + 1/8 (z^-4) – 1/3 (z^-10)

= d/ dz (6 z^-3/2) + d/ dz (1/8 (z^-4)) – d/ dz (1/3 (z^-10))

Apply the power rule i.e d/ dx xⁿ = nx^n-1

= 6 (-3/2) z^{-3/2 – 1} + 1/8 (-4) z^-4-1 -1/3(-10) z^-10-1

= -9z^-5/2 – 1/2 z^-5 + 10/3 z^-11

d/ dz ( 6 / √z³ + 1 / (8z⁴) – 1 / (3z¹⁰)) = -9z^-5/2 – 1/2 z^-5 + 10/3 z^-11

Find a variety of Other free Maths Calculators that will save your time while doing complex calculations and get step-by-step solutions to all your problems in a matter of seconds.

FAQs on Derivative Calculator

1. What is derivative formula?

Derivative is the fundamental tool of calculus. The derivative of a function of a real variable measures the sensitivity to change a quantity which is determined by another quantity. Derivative formula is

f¹(x) = lim_△x→0 ([f(x) + △x) – f(x)] / △x

2. What is the purpose of derivatives?

Derivatives are the financial contracts whose value is linked to the value of an underlying asset.

3. How do you find the derivative on a calculator?

Enter the input function in the calculator and hit on the calculate button which is provided next to that input box to get the output instantly.

4. Find the derivative of f(x). Where f(x) = 6x³ – 9x + 4?

f'(x) = 6.3 x^3-1 -9(1) + 0

= 18 x² -9

Chemical Equation Calculator

December 15, 2020 by Veerendra

Chemical Equation Calculator is a free online tool that displays the structure, balanced equation, equilibrium constant, substance properties with chemical names and formulas. LearnCram is providing online chemical equation calculator tool makes the prediction faster and easier and it displays the answer in a fraction of seconds.

How to Use Chemical Equation Calculator?

The procedure to use the chemical equation calculator is as follows:
Step 1: Enter the chemical equation in the input field
Step 2: Now click the button “Balance” to get the balanced equation
Step 3: Finally, the balanced equation, structure, equilibrium constant for the given chemical equation will be displayed in a new window

What is the Chemical Equation?

A chemical equation is defined as the symbolic representation of the chemical reaction where the reactants are written on the left side and the products are written on the right side. The reactants and products are separated by arrow symbols. Each unique substance in the chemical reaction is separated by a plus sign (+).
Example: 2 HCl + 2 Na → 2 NaCl + H₂

Example

Question:
Balance the given chemical equation: CH₄ + O₂ → CO₂ + H₂O
Solution:
Given chemical reaction: CH₄ + O₂ → CO₂ + H₂O
The balanced equation for the given chemical equation is:
CH₄ + 2 O₂ → CO₂ + 2 H₂O