Construction of a function

Asked Oct 24 '14 at 18:00

Active Oct 24 '14 at 18:00

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Give an example of a function that is partial differentiable and differentiable but not continuous partial differentiable .

One example I thought (but is wrong) is the function: $$f(x, y)=\left\{\begin{matrix} \dfrac{xy}{x^2+y^2} &,\left ( x, y \right )\in \mathbb{R}^2\setminus\left \{ \left ( 0,0 \right ) \right \} \\ 0 &, (x, y)=(0, 0) \end{matrix}\right.$$

Now I don't have any ideas on how to construct any function. Any ideas?

asked Oct 24 '14 at 18:00

Tolaso

Just consider the standard one variable example. – Git Gud Oct 24 '14 at 18:14
What do you mean? – Tolaso Oct 24 '14 at 18:20
See this. – Git Gud Oct 24 '14 at 18:22
How does this help? I am aware of that example in one-variable calculus? – Tolaso Oct 25 '14 at 05:56
That function is partially differentiable, differentiable, but its partial derivative (which coincides with the derivative) is not continuous. – Git Gud Oct 25 '14 at 09:42

Construction of a function

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