Question

What is the derivative of `f(x)=cos^2(x^3)`?

Answer 1

`f'(x)=-6x^2cos(x^3)sin(x^3)`

Explanation:

Use the Chain Rule.

`f'(x)=2cos(x^3)d/(dx)[cos(x^3)]`

Now, using the chain rule again, we can find `d/(dx)[cos(x^3)]`.
`d/(dx)[cos(x^3)]=-sin(x^3)d/(dx)[x^3]=-3x^2sin(x^3)`

So, `f'(x)=2cos(x^3)*-3x^2sin(x^3)=-6x^2cos(x^3)sin(x^3)`