Answer
$\frac{dV}{ds} = 108$ $cm^{2}$
Work Step by Step
The exercise is simply asking for the rate of change in volume $V$ with respect to its sides $s$. Therefore, it's merely a matter of finding the first derivative of the function: $$V = s^{3}$$ $$(\frac{d}{ds})V = s^{3} (\frac{d}{ds})$$ $$\frac{dV}{ds} = 3s^{3 - 1} = 3s^{2}$$ For the value $s = 6cm$: $$\frac{dV}{ds} = 3(6)^{2} = 3(36) = 108 cm^{2}$$
