Question

How do you differentiate `Sin ^ 3 x`?

Answer 1

`dy/dx = 3sin^2(x) *cos x`

Explanation:

In order to differentiate `sin^3(x)`, we need to use a chain rule, which tells us that

`d/dx[f(g(x))] = f'(g(x))*g'(x)`

Letting `y = sin^(3)(x)`, then

`dy/dx = 3sin^2(x) *cos x`

In this problem, we've also performed the power rule, namely by subtracting `1` from the power of `3` on the `sin x` term, which is why we end up with a `sin^2(x)`.