Question

What is the derivative of `y=cos^4(x^2)`?

Answer 1

`-8 x cos x cos ^2 x^2 sin x^2`

Explanation:

Using the quotient rule:

`d/dx cos ^ 4 x^ 2= 2 cos^2 x^2 d/dx cos ^ 2 x^ 2`

further:

`= 2 * cos ^ 2( x^ 2) {2 * cos x d/dx cos x^ 2 }`

now applying the chain rule we get :

= `-8 x cos x cos ^2 x^2 sin x^2`