×

# Lots of Derivatives

Prove that $$\left.\dfrac{d^n}{dx^n}\right|_{x=0}x^n\times n^x=n!$$ for all positive integer $$n.$$

Find, with proof, $$\dfrac{d^n}{dx^n}\dfrac{x^n}{1-x}.$$

Find, with proof, $$\dfrac{d^n}{dx^n}x^{n-1}\log x.$$

Note by Trevor B.
2 years, 2 months ago