What is the derivative of sin²(x)?

Solution:

Let us now use trigonometric identities to find the given derivative.

Let f(x) = sin²(x)

This can be written as: 

f(x) = f(u) = u² 

Thus, u = sin(x) -------------------- (1)

Also, du/dx = d(sin(x))/dx = cos(x) --------------------- (2)

Differentiating f(u) we get,

f'(u) = 2u · du/dx ---------------- (3)

Substituting (1) and (2) in (3) we get,

f'(u) = 2sin(x)cos(x)      

Therefore, the derivative of sin²(x) = 2sin(x)cos(x).

What is the derivative of sin²(x)?

Summary:

The derivative of sin²(x) = 2sin(x)cos(x).