Hello,(adsbygoogle = window.adsbygoogle || []).push({});

My question is as follows: Show that the function f(x,y) = sqrt(abs(xy)) is not differentiable at (0,0).

I was going to go with trying to show that the directional derivatives don't all exist here, but that would require finding the gradient, and I always get confused when trying to take the derivative of an absolute value. Essentially, this means that for xy larger than 0, f = sqrt(xy) and for xy smaller than 0, f = sqrt(-xy). But, of course, you can't have the square root of a negative number, so I'm confused....what should I do?

Thanks,

W.

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

Join Physics Forums Today!

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

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

# Homework Help: Derivative of absolute value

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