Question

How do you differentiate `Cos^4(2x)`?

Answer 1

`dy/dx=-8cos^3 2xsin2x`

Explanation:

For a function `y=[fg(x)]^n`, `dy/dx=n[f(x)]^(n-1)(f'(g(x)))(g'(x))`

In essence, we apply the power rule to the whole function and multiply it by the derivatives of the function in the brackets; in this case, `cos(2x)`.

Let `y=cos^4(2x)`

`dy/dx=4cos^3 2x(-sin2x)(2)=-8cos^3 2xsin2x`