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**transgalactic** i have this function

$\displaystyle f(x,y)=\begin{cases}x^{2}+y^{2}ln(x^{2}+y^{2}) & (x,y)\neq(0,0)\end{cases}$

and f(x,y)=0 on point (0,0)

i dont know the proper english term

i need to prove that f(x,y) is deferentialbe

so by the definition

$\displaystyle f(x,y)-f(0,0)-f_{x}(x-0)-f_{y}(y-0)=\epsilon_{1}(x-0)+\epsilon_{2}(y-0)$

and i need to find those epsilons which will make the sude to be equal

and both epsilons will go to zeroo when x and y are going to zero

i dont know what to put instead of "f" in each term

because the function is stplitted