Chapter 11, Problem 39RE

(a)

To determine

The Taylor series expansion of $f\text{'}\left(x\right)$ at $x=0$, where $f\left(x\right)=1+x^2+x^4+\mathrm{...}$.

(b)

To determine

A simple formula for $f\text{'}\left(x\right)$ at $x=0$ not involving a series, where $f\left(x\right)=1+x^2+x^4+\mathrm{...}$.