The second one is an example our instructor gave us, but I can't figure out where she got the "0" for cos and sin -

With this problem, we try to find the derivative of the inverse of f(x) where g(x) is the inverse:

$\displaystyle f(x)=x^3+3\sin{x}+2\cos{x}$

$\displaystyle g(x)=f^{\neg1}(x)$

$\displaystyle g^\prime(2)=?$

$\displaystyle f^\prime(x)=3x^2+3\cos{x}-2\sin{x}$

$\displaystyle 2=x^3+3\sin{x}+2\cos{x}$

Now here's the part where she skipped a lot of stuff

(SiMoon says : I don't think she did, you'll see below ) and literally put this on the board:

$\displaystyle \cos{0}=1$

$\displaystyle \sin{0}=0$

$\displaystyle g^\prime(2)=\frac{1}{3}$

Where did she get "0" from? I have no idea where that fits into the problem.

Any help I can get would be awesome, even if it's just a hint.

Thanks!