Let $\displaystyle s(x) = x - \frac{x^3}{3!} + \frac{x^5}{5!} - ... $and $\displaystyle c(x) = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} -$ ... for x in R.

Prove that s' = c and c' = s.

I think you are supposed to differentiate term by term but i'm not sure exactly how that is done.

Thanks