Related Rates

In a related-rate problem, two or more quantities are changing simultaneously with respect to time, and you are given the rate of change of one of them in order to find the rate of change of another. The quantities are typically linked by an equation — say $y = f(x)$ — where $x$ itself varies with time $t$.

Since $y$ depends on $x$ and $x$ depends on $t$, the chain rule connects all three rates of change: