Chapter 2 - Differentiation - 2.3 Exercises - Page 126: 84

$\frac{dV}{dt}=\frac{3\pi}{4}\sqrt t+\frac{\pi}{2\sqrt t}$

$V=\pi r^2h$ $V=\pi (\sqrt{t+2})^2(\frac{1}{2}\sqrt t)$ $V=(t+2)(\frac{\pi}{2}\sqrt t)$ $V=\frac{\pi}{2}t^{\frac{3}{2}}+\pi t^{\frac{1}{2}}$ $\frac{dV}{dt}=(\frac{3}{2})\frac{\pi}{2}t^{\frac{1}{2}}+(\frac{1}{2})\pi t^{-\frac{1}{2}}$ $\frac{dV}{dt}=\frac{3\pi}{4}\sqrt t+\frac{\pi}{2\sqrt t}$