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Question: partial derivative of a piecewise function

Question:partial derivative of a piecewise function

annarita 15 Maple
differentiation diff piecewise homework
July 18 2024
0

I want to obtain the partial derivative of a piecewise function. How it is possible to calculate  the derivative in (0,0) with diff?

I should get, as answer,  a new piecewise function

with(student);
f := (x, y) -> piecewise((x, y) = (0, 0), 0, (x^3*y - x*y^3)/(y^2 + x^2));
 f := proc (x, y) options operator, arrow; piecewise((x, y) = 

    (0, 0), 0, (x^3*y-x*y^3)/(y^2+x^2)) end proc

fx := (x, y) -> diff(f(x, y), x);
fx := proc (x, y) options operator, arrow; diff(f(x, y), x) end 

   proc

fx(0, 0);
Error, (in fx) invalid input: diff received 0, which is not valid for its 2nd argument

but i obtain an error

anna rita
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