# Thread: Differentiate a function with two variables

1. ## Differentiate a function with two variables

I know this is a easy question, but I just don't know how to solve it using definition of differentiability. Help please.

Using the DEFINITION of DIFFERENTIABILITY (not the FUNDAMENTAL LEMMA!!!) show that the function
f(x,y)=xy
is differentiable at the point (1,2).

2. The problems asks you to use the definition, so use it !
Tell us where did you stuck.

3. I don't know the definition of differentiation for 2 variables so that's why I get stuck. I only know it for single variable but then I cannot deduce this for two.

4. Originally Posted by nbluo
I don't know the definition of differentiation for 2 variables so that's why I get stuck. I only know it for single variable but then I cannot deduce this for two.
If a function can be differentiated at a point, what does that actually mean? Well this means that we have a function whose left and right limits are equal.

In symbols we have,

$\lim_{x \to 1^{-}} \lim_{y \to 2^{-}}f(x,y) = \lim_{x \to 1^{+}} \lim_{y \to 2^{+}} f(x,y) = f(1,2)$