Question

How do you differentiate `f(x)=sqrt(cos^3(3x-2))` using the chain rule?

Answer 1

The answer is `=(-9sin(3x-2)cos^2(3x-2))/(2sqrt(cos^3(3x-2)`

Explanation:

The derivative of `(sqrtx)'=1/(2sqrtx)`
and the derivative os `(cosx)'= -sinx`
As `f(x)=sqrt(cos^3(3x-2))`
So using the chain rule

`f'(x)=1/(2sqrt(cos^3(3x-2)))`*`(3cos^2(3x-2))` `(-sin(3x-2))*3`