## Calculus (3rd Edition)

$2\sqrt {3}\,cm/s$
Let the diagonal of the cube be $r$ and its edge be $a$. We are given that $\frac{da}{dt}=2\,cm/s$ The length of the diagonal of a cube with edge length equal to $a$ is $\sqrt {3}a$. That is, $r=\sqrt {3}a$ $\frac{dr}{dt}=\frac{dr}{da}\times\frac{da}{dt}=\frac{d}{da}(\sqrt {3}a)\times2\,cm/s$ $=2\sqrt {3}\,cm/s$