Suppose . Then is differentiable at a point if there is an n by m matrix such that .
My question is, does it matter HOW goes to 0? For example, consider the function . Say I wanted to calculate its derivative.
When taking the limit of the derivative difference quotient, is it permissible to let the entries of the matrix approach 0 in any fashion I want?
I am asking this because I am just learning multi-variable calculus, and when calculating the derivatives I've always let = (h h) and was wondering if I am allowed to do this.