TITLE: $100$-th derivative of the function $f(x)=e^{x}\cos(x)$
QUESTION [68 upvotes]: I've got this task I'm not able to solve. So i need to find the 100-th derivative of $$f(x)=e^{x}\cos(x)$$ where $x=\pi$.
I've tried using Leibniz's formula but it got me nowhere, induction doesn't seem to help either, so if you could just give me a hint, I'd be very grateful.
Many thanks!

REPLY [2 votes]: I'm a little late to the game, but you can check your work in Wolfram Alpha with this query:
D[E^x Cos[x], {x, 100}]  at x = pi

which matches the answer posted by @choco_addicted. The syntax comes from the Wolfram Language page for the D function.