Question

find the derivative,y=ln(cos^2theta) help please!

Answer 1

derivative if log(f(x)) is f'(x)/f(x)

use the fact that

\[\cos^2 \theta = (\cos(\theta))^2\]

\[dy/dx = -2\sin(\theta)/(\cos^2 \theta)\]

this can be simplified to

\[dy/d \theta = -2\sin \theta/\cos \theta \times 1/\cos \theta\]

or \[dy/d \theta = -2\tan \theta \sec \theta\]

Answer 2

I think the derivative of cos^2 theta is:

so f'(x)/f(x) = -2*tan(theta)