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Derivative Calculator

Enter the function and variable to find the derivative using derivative calculator.

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Differentiation calculator is an online calculus tool that finds the derivative of a given function. It can perform explicit differentiation one click. If you are looking for implicit differentiation, use our implicit differentiation calculator.

Most importantly, this differential calculator shows the step by step calculation along with the detailed answer.

Derivative – Definition

Let f(x) be a function whose domain contains an open interval at some point x0. The function f(x) is said to be differentiable at x0, and the derivative of f(x) at x0 is given by:

derivative

In other words, derivative measures the sensitivity to change of the function value with respect to a change in its argument. The reverse function of derivative is known as antiderivative.

differentiation

How to calculate derivative?

To differentiate a function, let’s calculate the derivative of 1/x to grasp the basic idea of derivation.

As 1/x = x-1

We will use product rule (refer to below rules).

d/dx (x-1) = -1(x-2) = - 1/x2

Example:

Find the derivative of (x+7)2.

Solution:

Step 1: Apply derivation symbol.

derivation

Step 2: Apply power rule.

differential calculation

power rule

derivative calc

result of derivative

Some functions need second derivative to complete the process of differentiation. You can use our second derivative calculator in this case.

Derivative rules – Formulas

  • Constant Rule

constant rule

  • Power Rule

power rule

  • Sum Rule

Sum rule

  • Product Rule

product rule

  • Quotient Rule

quotient rule

  • Chain Rule

chain rule

  • Trigonometric Derivatives

trigonometric rules

  • Derivative of e^x (Exponential)

exponential rule

  • Logarithm Derivatives

log rule for derivative

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