Hello Forumites,

The partial derivatives of order r of an analytic function $f(x_1,...x_n)$ of n variables do not depend on the order of differentiation but only on the number of times that each variables appears.And hence there exists $\binom{n+r-1}{r}$ different partial derivatives of rth order. A function of three variables has fifteen derivatives of fourth order and 21 derivatives of fifth order.

What does this means? If any one knows, he may reply.