Derivative of a series I am having trouble with a homework (so no full solutions please) question. Having trouble starting, so if someone could point me in the right direction, I would really appreciate it.

f(x) = x - $\frac{x^3}{3!}$ + $\frac{x^5}{5!}$ - $\frac{x^7}{7!}$ + ... Find the smallest value of n such that f$^{(n)}$ = f(x). 

I am unsure how to handle this since it appears to be a series.
For power series like this, it turns out that you can differentiate term-by-term; the formal justification takes a bit of work - but for this series, the radius of convergence is infinite, so differentiating termwise will work.

To get you started, note that

\begin{align*}
f'(x) &amp;= \frac{d}{dx} x - \frac{d}{dx} \frac{x^3}{3!} + \frac{d}{dx} \frac{x^5}{5!} - \dots \\
&amp;= 1 - \frac{3 x^2}{3!} + \frac{5x^4}{5!} - \dots \\
&amp;= 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \dots
\end{align*}
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