so, i have two really similar questions here:

1) using the maclaurin series for $\displaystyle e^x$, show that $\displaystyle (e^x)' = e^x$

and 2) using the maclaurin series for $\displaystyle sin(x)$, show that $\displaystyle (sin(x))'= cos(x)$

i know what these are, but, i have no idea how to show what they're asking

any help would be greatly appreciated!