Question

Find the derivative of sin2x by the first principle

Answer 1

derivative of sin2x is in pictures

Answer 2

sin^2x can be expressed as (sin x)^2

Let f(x) = (sin x)^2

It can be written as f(u) = u^2 x where u = sin x.

f´(u) = 2u and u´= cos x

so that multiplying together we get

f´(x) = 2u·cos x = 2 sin x cos x

Answer

The derivative of sin2x = 2 sin x cos x