Question

What is the derivative of `(-sinx^2)/2`?

Answer 1

`d/dx( -sinx^2/2) = -x cosx^2`

Explanation:

Using the chain rule with `u= x^2`:

`d/dx( -sinx^2/2) = -1/2 d/(du) (sinu) xx (du)/dx`

`d/dx( -sinx^2/2) = -1/2 cosx^2 xx (dx^2)/dx`

`d/dx( -sinx^2/2) = -1/2 cosx^2 xx 2x`

`d/dx( -sinx^2/2) = -x cosx^2`