1. ## Partial differentiation

Let $V =\pi r^{2}h, S = 2\pi r(r+h)$

Compute the following

$\frac{\partial V}{\partial h}|_{S}, \frac{\partial V}{\partial S}|_{r}, \frac{\partial S}{\partial V}|_{r}$

That is for the first partial derivative hold $S$ constant and so on for the other two partial derivatives.

So for the first one, am I suppose to solve $V$ in terms of $S$? I am not sure how to go about computing those partial derivatives. Thank you.

2. $
\frac{\partial V}{\partial h}|_{S}
$

You must have V(S,h).
Eliminate r from V(r,h) using S(r,h).

3. And how would I go about doing that, exactly? Since a $r^{2}$ and a $r$ appear in the expression of $S$.