- #1
wakko101
- 68
- 0
Hello,
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.
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.