In differential calculus, related rates problems involve ratios of derivatives of two or more related variables that are changing with respect to time.
For example, suppose x and y are both differential functions of time t and are related by the equation
and you are supposed to find dy/dt when x = 3, given that dx/dt = 2 when x = 3.
First, differentiate both sides of the equation with respect to t:
![{d \over dt}[y] = {d \over dt}[x^3 + 5].\,](a/../upload/math/3333d5a58381ee67fdcd8351724aa1b4.png)
Next, apply the chain rule:
Finally, substitute 3 for x and 2 for dx/dt:
