Consider $w=2x+y^2z$ with $x=p\cos\theta\sin\phi$, $y=p\sin\theta\cos\phi$, $z=p\cos\theta$. Find the partial derivatives $w_p$,$w_\theta$, $w_\phi$, each in terms of only the independent variables $p,\theta,\phi$.
I'm really lost on how to do this, I' not sure if I take $w_p=\frac{dw}{dx}\frac{dx}{dp}+\frac{dw}{dy}\frac{dy}{d\theta}+\frac{dw}{dz}\frac{dz}{d\phi}$
hint
replacing $x,y,z$ in $ w $, we get
$$w=2p\cos(\theta)\sin(\phi)+$$ $$p^3\sin^2(\theta)\cos(\theta)\cos^2(\phi)$$ thus $$\frac{\partial w}{\partial p}=2\cos(\theta)\sin(\phi)+$$ $$3p^2\sin^2(\theta)\cos(\theta)\cos^2(\phi)$$