Chapter 11.9, Problem 2PT

For $f(x)={\displaystyle \underset{n=0}{\overset{\infty }{\sum }}\frac{x^{2n}}{n!}}$, f′(x) =

1. a) ${\displaystyle \underset{n=1}{\overset{\infty }{\sum }}\frac{x^{2n-1}}{n!}}$
2. b) ${\displaystyle \underset{n=1}{\overset{\infty }{\sum }}\frac{2x^{2n-1}}{(n-1)!}}$
3. c) ${\displaystyle \underset{n=1}{\overset{\infty }{\sum }}\frac{2^n{x}^{2n-1}}{n!}}$
4. d) ${\displaystyle \underset{n=1}{\overset{\infty }{\sum }}\frac{(2n-1)x^{2n-1}}{(n-1)!}}$