What is the derivative of sin² x?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The process of determining the derivative is known as differentiation whereas the inverse process is known as anti-differentiation.

Derivatives are defined as the varying rate of change of a function with respect to an independent variable.

The derivative is basically used when there is some varying quantity, and the rate of change is not constant.

Table of content

It is used to measure the sensitivity of one variable (dependent variable) with respect to another variable (independent variable).

Derivatives can be classified into various types based on their order such as first and second-order derivatives.

Consider y = sin² x

Using the chain rule, differentiate both sides with respect to x

dy/dx = d/dx sin² x

dy/dx = 2 sin x X d/dx sin x [As d/dx xⁿ = nxⁿ⁻¹]

dy/dx = 2 sin x X cos x [As d/dx sin x = cos x]

dy/dx = 2 sin x cos x

dy/dx = sin 2x [As 2 sin x cos x = sin 2 x]

Therefore, the derivative of sin² x is sin 2x.

Summary:

The derivative of sin² x is sin 2x.

Related Questions:-

What is the derivative of sin2 x?