The Maclaurin series for ln(1+x)\ln(1+x)ln(1+x) is ∑n=1∞(−1)n+1nxn\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n}x^n∑n=1∞n(−1)n+1xn (for −1<x≤1-1 < x \leq 1−1<x≤1). What is ddxln(1+x)\frac{d}{dx}\ln(1+x)dxdln(1+x) expressed as a power series?
∑n=1∞(−1)n+1xn−1\sum_{n=1}^{\infty} (-1)^{n+1} x^{n-1}∑n=1∞(−1)n+1xn−1
∑n=0∞(−1)nxn\sum_{n=0}^{\infty} (-1)^n x^n∑n=0∞(−1)nxn
∑n=1∞(−1)n+1nxn−1\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n}x^{n-1}∑n=1∞n(−1)n+1xn−1
∑n=0∞(−1)nn+1xn\sum_{n=0}^{\infty} \frac{(-1)^{n}}{n+1}x^{n}∑n=0∞n+1(−1)nxn