Question

$V=\frac{1}{3}\pi (l^{2}H-H^3)$ . Find $\frac{d}{dx}\left(H^3\right)$

Answer 1

$V=\frac{\pi }{3}(l^{2}H-H^3)$

$dV=\frac{\pi }{3}\left(\frac{d}{dx}\right(l^{2}H)-\frac{d}{dx}(H^3\left)\right)$

$\frac{d}{dx}\left(l^{2}H\right)=2l\frac{dl}{dx}\times H+l^2\frac{dH}{dx}$

$\frac{d}{dx}\left(H^3\right)=3H^2\frac{dH}{dx}$