The volume of a spherical balloon of radius r cm increases at a rate of $10\pi cm^3/s$.Find the rate of change of its radius.
The answer: Let $V cm^3$ be the volume of the balloon at time $t$.
$$V=\frac43 \pi r^3$$
$\frac{dV}{dt}=\frac43 \pi(3r^2)\frac{dr}{dt}$ (which is equal to $\frac{dV}{dr}\frac{dr}{dt}$).
and so on. What I don't get is how $\frac{dV}{dr}\frac{dr}{dt}$came from.There are only three variables here,so messing them around could already get the answer.But what if there are more variables in a rate of change question?How do I write a good equation?