E^z - xyz = 0       dz/dy=? dz\dx=?

[latex]e^z-xyz=0;\\ d(e^z-xyz)=de^z-dxyz=e^zdz-xydz-xzdy-yzdx=\\ =(e^z-xy)dz-xzdy-yzdx=0;\\ (e^z-xy)dz-xzdy-yzdx=0;\\ (e^z-xy)\frac{dz}{dx}-xz\frac{dy}{dx}-yz=0;\frac{dy}{dx}=0;\\ \frac{dz}{dx}= \frac{yz}{e^z-xy};\\ (e^z-xy) \frac{dz}{dy}-xz-yz\frac{dx}{dy}=0;\frac{dx}{dy}=0;\\ \frac{dz}{dy}= \frac{xz}{e^z-xy} [/latex]