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Math Help - Differentiate a function with two variables

  1. #1
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    Post 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).
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  2. #2
    Super Member General's Avatar
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    The problems asks you to use the definition, so use it !
    Tell us where did you stuck.
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  3. #3
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    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.
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  4. #4
    Senior Member AllanCuz's Avatar
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    Quote Originally Posted by nbluo View Post
    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)
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