Well, it looks simple, but I'm not sure If the answer I'm giving is right.

The function is:

$\displaystyle f(x,y)=\sin|y|$

And it asks for the partial derivatives, so:

$\displaystyle \displaystyle\frac{\partial f}{\partial x}=0$

And

$\displaystyle \displaystyle\frac{\partial f}{\partial y}=\begin{Bmatrix}{ \cos|y|}&\mbox{ if }& y>0\\\not{\exists & \mbox{if}& y=0\\-\cos|y| & \mbox{if}& y<0\end{matrix}$

Is this right?