Question

How do you differentiate `cos(x^2)`?

Answer 1

`- 2x sin x^2`

Explanation:

Use the chain rule

so `y = cos u implies dy/(du) = -sin u`

`u = x^2 implies (du)/dx = 2x`

Chain rule `dy/dx = dy/(du)* (du)/dx`

`= - sin u * 2x = - 2x sin x^2`