Directional Derivative for a piece-wise Function – math.stackexchange.com

Directional Derivative for a piece-wise Function – math.stackexchange.com

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Consider the function $f:\mathbb{R}^2 \rightarrow \mathbb{R}$ given by $$f(x,y)=\begin{cases} \frac{xy}{x^2+y^2} &\text{if} (x,y)\neq (0,0)\\ 0 &\text{if} (x,y)=(0,0) \end{cases}$$ For which ...

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