Question

How do you find the derivative of `y= 6cos(x^2)` ?

Answer 1

By Chain Rule, `y'=-12sin(x^2)`.

Recall: Chain Rule
`[f(g(x))]'=f'(g(x))cdot g'(x)`

In the posted function,
`f(x)=6cos x` and `g(x)=x^2`
By taking the derivative,
`f'(x)=-6sin x` and `g'(x)=2x`

Now, we have
`y'=-6sin(x^2)cdot 2x=-12sin(x^2)`