Chapter 9.10, Problem 2QCE

$\begin{array}{l}\frac{d}{dx}\left[{\displaystyle \underset{k=1}{\overset{\infty }{\sum }}{(-1)}^{k+1}\frac{x^k}{k}}\right]=\text{\_\_\_\_\_}+\text{\_\_\_\_\_}x+\text{\_\_\_\_\_}{x}^2+\text{\_\_\_\_\_}{x}^3\\ +\mathrm{...}={\displaystyle \underset{k=0}{\overset{\infty }{\sum }}\text{\_\_\_\_\_}}\end{array}$