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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

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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

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  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.



    Answer  :  

    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.



    Answer  :  

    1.



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