The function $ f(x,y)=0$ $if$ $x,y≠0$ $and$ $ f(x,y)=1$ $if$ $ x,y=0$ is given. I have to prove that partial derivative of $x$ and partial derivative of $y$ exist at the beginning of the axes and find them.I am confused about how we find the derivatives.
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The specification of $f(x,y)$ is unclear. Do the commas in “$x,y$” mean and or or? – Hans Lundmark Jun 02 '18 at 08:41
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I meant x AND y ,the function consists of two variables – Deppie3910 Jun 02 '18 at 10:41
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2If it's and in both cases, then you haven't specified $f(x,y)$ for all $(x,y)$. You need and in one case and or in the other! – Hans Lundmark Jun 02 '18 at 11:50
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Partial derivatives exist for any $ (a,b)\neq(0,0)$, let proceed by the definition
$$f_x=\lim_{h\to0}\frac{f(a+h,b)-f(a,b)}{h}$$
$$f_x=\lim_{h\to0}\frac{f(a,b+h)-f(a,b)}{h}$$
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