### Home > APCALC > Chapter 7 > Lesson 7.1.4 > Problem7-38

7-38.

Let $S$ be the surface area of an inflatable cube with sides of length $x$ at time $t$. Write an equation that relates $\frac { d S } { d t }$ to $\frac { d x } { d t }$.

$S = 6x^2$

Implicitly differentiate with respect to time, $t$.

$\frac{dS}{dt}=\frac{d}{dt}(6x^{2})=12x\frac{dx}{dt}$