Question

How do you differentiate `f(x)=sin^2x/cos^2x`?

Answer 1

`f'(x) = 2sec^2xtanx`

Explanation:

We know that `sintheta/costheta = tantheta`. So `f(x) = sin^2x/cos^2x = tan^2x = (tanx)(tanx)`.

We know the derivative of `tanx` is `sec^2x`. By the product rule;

`f'(x) = sec^2xtanx + sec^2xtanx`

`f'(x) = 2sec^2xtanx`

Hopefully this helps!