Chapter 9.10, Problem 22ES

Confirm the derivative formula by differentiating the appropriate Maclaurin series term by term.

$\begin{array}{l}\left(\text{a}\right)\frac{d}{dx}[\sinh x]=\cosh x\\ \left(\text{b}\right)\frac{d}{dx}[{\tan }^{-1}x]=\frac{1}{1+x^2}\end{array}$