$z=x^2+xy^3, x=uv^3+w^2, y=u+ve^w$, Find the partial derivatives $\frac{\partial z}{\partial u},\frac{\partial z}{\partial v},\frac{\partial z}{\partial w}$ when $u=1,v=2,w=0$
$$ \frac{\partial z}{\partial u}=2x\frac{\partial x}{\partial u}+y^3\frac{\partial x}{\partial u}+3xy^2\frac{\partial y}{\partial u} $$ How do I deal with it since we have I think 6 variables, any hints would be helpful.