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 (x
^{n}) = 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) / (g
^{2}) [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) = sec
^{2}(x) - d/dx cot(x) = -cosec
^{2}(x)

**Example**

**Question: Solve derivative of 6 / √z ^{3} + 1 / (8z^{4}) – 1 / (3z^{10})**

**Solution:**

Given function is 6 / √z^{3} + 1 / (8z^{4}) – 1 / (3z^{10})

d/ dz ( 6 / √z^{3} + 1 / (8z^{4}) – 1 / (3z^{10})) = ?

= 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 x^{n} = 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 / √z^{3} + 1 / (8z^{4}) – 1 / (3z^{10})) = -9z^{-5/2} – 1/2 z^{-5} + 10/3 z^{-11}

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### 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

f^{1}(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) = 6x ^{3} – 9x + 4?**

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

= 18 x^{2} -9