Question

e^z - xyz = 0       dz/dy=? dzdx=?

Answer 1

$e^z-xyz=0;\ d(e^z-xyz)=de^z-dxyz=e^zdz-xydz-xzdy-yzdx=\ =(e^z-xy)dz-xzdy-yzdx=0;\ (e^z-xy)dz-xzdy-yzdx=0;\ (e^z-xy)frac{dz}{dx}-xzfrac{dy}{dx}-yz=0;frac{dy}{dx}=0;\ frac{dz}{dx}= frac{yz}{e^z-xy};\ (e^z-xy) frac{dz}{dy}-xz-yzfrac{dx}{dy}=0;frac{dx}{dy}=0;\ frac{dz}{dy}= frac{xz}{e^z-xy}$