Partial Derivative fy(x,y): What Is It?

[squenshl]

Given that f(x,y) = x|y|
I know that f_x(x,y) = |y| but what is f_y(x,y).
Thanks heaps.

 

[dx]

Hint: Break it up into two cases: If y > 0, then f(x,y) = xy. If y < 0, then f(x,y) = -xy.

 

[HallsofIvy]

Note that g(y)= |y| is not differentiable at y= 0 so f(x,y)= x|y| has no partial derivative, with respect to y, on the line y= 0.