- #1

absci2010

- 10

- 0

^{2}/(x

^{2}+y

^{2}) if (x,y)[tex]\neq[/tex](0,0)

=0 if (x,y)=(0,0)

Show that the partial derivatives of x and y exist at (0,0).

This may be a really stupid question, but would the partial derivatives of x and y at (0,0) just be 0? I tried taking that partial derivatives of xy

^{2}/(x

^{2}+y

^{2}) and got:

df/dx=[(x

^{2}+y

^{2})(y

^{2})-xy

^{2}(2x)]/(x

^{2}+y

^{2})

^{2}

and

df/dy=[(x

^{2}+y

^{2})(2xy)-xy

^{2}(2y)]/(x

^{2}+y

^{2})

^{2}

which i don't believe cancel out.

Please help?