Is a function of many variables differentiable at a point?

Question

Mathematical analysis

How to check if a function of many variables is differentiable at a point or not?

Answer 1

By definition: you need to prove that the increment of the function at this point can be represented as the sum of the value of the function at this point, plus the linear part with respect to the increment of the independent variable, plus an infinitesimal. In the form of a formula on the wiki: link