Derivative Calculator

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:

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.

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.

Step 2: Apply power rule.

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

• Power Rule

• Sum Rule

• Product Rule

• Quotient Rule

• Chain Rule

• Trigonometric Derivatives

• Derivative of e^x (Exponential)

• Logarithm Derivatives