Chapter 6.9, Problem 64ES

Show that

(a) $\frac{d}{dx}\left[{\mathrm{sech}}^{-1}\left|x\right|\right]=-\frac{1}{x\sqrt{1+x^2}}$

(b) $\frac{d}{dx}\left[{\mathrm{csch}}^{-1}\left|x\right|\right]=-\frac{1}{x\sqrt{1+x^2}}$ .