The problem is:

Prove that the mixed partial derivative f xy (0,0) isequal to the mixed partial derivative f yx (0,0) ,not

given the function:

f(x,y) = x.y when |x|>=|y|

= -x.y when |x|<|y|

Friends, I have tried a few times but am always landing up by proving the opposite, ie, f xy (0,0) = f yx (0,0), which is not right.

One has to use the first principles to find these derivatives at the point (0,0).

If one uses the differentiation formulae then one lands up with 0/0 undefined form.

Kindly help.