By writing $|x|=\sqrt{x^2}$ and using the Chain Rule, one can verify that $\frac{d}{dx}|x|=\frac{x}{|x|}$.
(a) If $f(x)=|\sin{x}|$, find $f'(x)$.
(b) Where is $f(x)$ not differentiable? Merely give the smallest positive value of $x$.
(c) If $g(x)=\sin{|x|}$, find $g'(x)$.
(d) Where is $g(x)$ not differentiable?
(a) $f'(x) =$
(b) At $x=$
(c) $g'(x) =$
(d) At $x=$

You can earn partial credit on this problem.