# Partial derivatives in multivariable function

I was doing some practice problems and everything was going great till I saw this question out of the ordinary: $$f(x,y) = \sum_{n=0}^\infty(xy)^n \qquad \left|xy\right| < 1$$ Any thoughts on how to do this?

I know that the general formula should be something like this: Differentiate with respect to $x$: $nx^{n-1}y^n$

But this whole summation thing really confuses me as I am not 100% sure what to do.

• Just sun the series first as in then hint and the find the derivative. – Mhenni Benghorbal Sep 27 '13 at 7:14
• would it be converge to 1/(1-xy) ?? – Raynos Sep 27 '13 at 13:34