TITLE: What is the $1469^\text{th}$ derivative of $x^{532}-5x^{37}-4$?
QUESTION [7 upvotes]: I'm doing some basic calculus exercises on higher derivatives. But I'm stuck at a problem. The question is to find the 1469th derivative of $f(x)=x^{532}-5x^{37}-4$. I've read something about using the general Leibniz rule and a binomial but I can't get my head around it.

REPLY [26 votes]: Hint: $(x^n)^{(k)}=0$ if $k>n$, $k,n\in\mathbb{Z}_+$.