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Derivative Calculator
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Differentiation can be stated as derivative of a function. Derivative Calculator is used to calculate the derivative of a function with respect to the given variable and derivatives up to the order 10th. Try our free Derivative Calculator and get your problems solved instantly.

Below is given a default differentiable function with respect to its derivative, click "Calculate". It calculates the derivative of the function with respect to its variable and derivative.

## Steps for Derivative

Step 1 :

Apply the formula:  f'(x) = $\lim_{\Delta x \to 0}$ $\frac{ f(x+\Delta x) – f(x)}{\Delta x}$
this equation is called differentiation equation. By using this equation, we can find derivatives of different functions. $\Delta$x is the small change in the variable x. f(x) is a function of x. f '(x) is derivative of f(x).

## Derivative Problems

1. ### Find the derivative of 7x + 10?

Step 1 :

If f(x) = 7x + 10 then f(x + $\Delta$ x) = 7(x + $\Delta$ x) + 10

=> f'(x) = $\lim_{\Delta x \to 0}$ $\frac{ f(x+\Delta x) – f(x)}{\Delta x}$

=> f'(x) = $\lim_{\Delta x \to 0}$ $\frac{ 7(x + \Delta x) + 10 – (7x + 10)}{\Delta x}$

=> f'(x) = $\lim_{\Delta x \to 0}$ $\frac{ 7x + 7 \Delta x + 10 – 7x - 10)}{\Delta x}$

=> f'(x) = $\lim_{\Delta x \to 0}$ $\frac{7 \Delta x }{\Delta x}$

=> f'(x) = $\lim_{\Delta x \to 0}$ 7

=> f'(x) = 7.

7.

2. ### Find the derivative of f(x) = x ?

Step 1 :

If f(x) = x, then f(x + $\Delta$ x) = x +  $\Delta$ x

=> f'(x) = $\lim_{\Delta x \to 0}$ $\frac{ f(x+\Delta x) – f(x)}{\Delta x}$

=> f'(x) = $\lim_{\Delta x \to 0}$ $\frac{ x + \Delta x – x}{\Delta x}$

=> f'(x) = $\lim_{\Delta x \to 0}$ $\frac{ \Delta x}{\Delta x}$

=> f'(x) = $\lim_{\Delta x \to 0}$ 1

=> 1.