Hi all,
As well-known result, (type in TeX format)
$f(x,y)=(x^3*y-y^3*x)/(x^2+y^2$
for $(x,y)\nq(0,0) and $f(0,0)=0$
has second-order partial derivatives, $f_{x,y}(0,0)=-1$ and $f_{y,x}
(0,0)=1$. Note they are not equal. But if use directly
diff(f,x,y).subs({x:0,y:0})
to compute the derivatives, it will get the wrong answer,1! As in
calculus we use normally, the result can be computed correctly:
1. calculate $f_x(0,0)$;
2. calculate the limit: $ (f_x(0,k)-f_x(0,0))/k$
This error comes from the the false computing procedure but not the
function itself. But how to prevent the error occurrence?
cch
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