Question

How do you find the derivative of `f(x)= cos^(4) (5x)`?

Answer 1

Remember that `cos^4(5x) = (cos(5x))^4` And apply the chain rule (twice).

Explanation:

`f'(x) = 4(cos(5x))^3 * d/dx(cos(5x))`

`= 4(cos(5x))^3 * [sin(5x)*d/dx(5x)]`

`= 4(cos(5x))^3 * [sin(5x)*(5)]`

`= 20cos^3(5x) sin(5x)`