# What is the derivative of sin^{2}(x)?

We’ll solve this derivative using the product rule of differentiation.

## Answer: The derivative of sin^{2}(x) = 2sin(x)cos(x)

Let us now use trigonometric identities to find the given derivative

**Explanation:**

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

This can be written as

f(x) = f(u) = u^{2}

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 sin^{2}(x) = 2sin(x)cos(x).

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