Question

How do you differentiate `f(x)=(cos^2x^2)^(7/3)` using the chain rule?

Answer 1

`-28/3xcos^(11/3)(x^2)sin(x^2)`

Explanation:

`f(x) = (cos^2x^2)^(7/3)`

`=(cos^(14/3)x^2)`

`f'(x) = 14/3* cos^(11/3)x^2 * d/dx(cosx^2)` (Power rule and Chain rule)

`= 14/3* cos^(11/3)x^2 * (-sinx^2) * 2x` (Chain rule)

`=-28/3xcos^(11/3)(x^2)sin(x^2)`