# How do you differentiate sin^{3}x?

Differentiation, also known as finding the derivative is the process of finding the instantaneous rate of change of a function.

## Answer: The value when we differentiate sin^{3}x is 3 sin^{2}x cosx.

Let's understand the steps to solve the given question.

**Explanation:**

According to the rules of differentiation,

d/dx(x^{n}) = nx^{n-1}

Thus,

d/dx(sin^{3}x) = 3 sin^{2}x d/dx(sin x) ----------------- (1)

We know that,

d/dx (sin x) = cos x

Substituting in (1) we get,

d/dx(sin^{3}x) = 3 sin^{2}x cos x

### Thus, the value when we differentiate sin^{3}x is 3 sin^{2}x cosx.