Differentiation Calculator

Differentiation is a method in Calculus which gives us the rate of change of the function value with respect to the change in the

variable of the function. Differentiation is a very important section in Calculus and Differentiation calculator is the quick online

tool which makes the calculations based on differentiation, easy and simple!


Example 1: Give the differentiation of the function, f(x) = x⁴ + lnx

To differentiate the above given function, we write it as

 df(x)/dx = d(x⁴)/dx + d(ln x)/dx

Power rule of the Derivatives   d f(xⁿ)/dx = n*x^n-1

Applying the above formula to the term x⁴, we get

 d f(x)/dx = 4 * x^4-1 + d (ln x)/dx

The derivative of ‘ln x’ expression is ‘1/x’

Hence the differentiation of the given function gives   4x³ + 1/x



Example 2: Give the differentiation of the function, f(x) = sin(x) + cos(x)

 To differentiate the above given function, we write it as

 d f(x)/dx = d sin(x)/dx + d cos(x)/dx

 Here we have to find the derivatives of the trigonometric functions.

Derivative of sin(x) = cos(x)

Derivative of cos(x) = -sin(x)

Hence d f(x)/dx = cos(x) – sin(x)

The differentiation of the given function d f(x)/dx = cos(x) – sin(x)