Chapter 2.5, Problem 43ES

In each part, determine where $f$ is differentiable.

(a) $f\left(x\right)=\sin x$

(b) $f\left(x\right)=\cos x$

(c) $f\left(x\right)=\tan x$

(d) $f\left(x\right)=\cot x$

(e) $f\left(x\right)=\sec x$

(f) $f\left(x\right)=\csc x$

(g) $f\left(x\right)=\frac{1}{1+\cos x}$

(h) $f\left(x\right)=\frac{1}{\sin x\cos x}$

(i) $f\left(x\right)=\frac{\cos x}{2-\sin x}$