Se the function to show that fx(0, 0) and fy(0, 0) both exist, but that f is not differentiable at (0, 0). f(x, y) = 9x2y x4 + y2 , (x, y) ≠ (0, 0) 0, (x, y) = (0, 0)

It is proved that exixts at (0,0) but not differentiable there.

Step-by-step explanation:

Given function is,

   exists.

And,

  exists.

 where m is a variable.

which depends on various values of m, therefore limit does not exists. So f(x,y) is not continuous at (0,0). Hence it is not differentiable at (0,0).

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