L.C. for this function

Question

I got stuck to show if this function $f(x,y)=|x|e^{xy}+x\sin(x+2y)$ satisfies Lipschitz condition or not. If found hard it to use the definition to do that. Clearly, the function is continuous but it is not differentiable at 0. Consider the regions one has the point $(0,y)$and the second does not have $(0,y)$ Any idea?