f(x,y)= xy(adsbygoogle = window.adsbygoogle || []).push({}); ^{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?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Partial Derivatives of Discontinuous Fcn?

**Physics Forums | Science Articles, Homework Help, Discussion**