This section focuses on the related rates concept and how to solve such kind of problems.

If a quantity y is a function of time t, the rate of change of y with respect to time is given by dy/dt. When two or more quantities are the functions of time and are related by an equation, the relation of their rates of change may be found by differentiating both sides of the equation. Here is an example:

Suppose water is running out of a conical funnel at the speed of 2 in³/sec. The radius of the base of the funnel is 5 in and the height 15 in. Find the rate at which the water level is dropping when it is 2 in from the top.

Let r be the radius and h the height of the surface of the water at time t, and let v be the volume of the water in the funnel.

By similar triangles, r/5 = h/15. Therefore, r = h/3.

Therefore the volume of the water in the funnel is

     v = πr²h/3 = πh³/27

Differentiate both side of the above equation.

     dv/dt = (πh²/9)(dh/dt)

The water runs out off the funnel at speed of 2 in³/sec, so dv/dt = -2. Thus,

     -2 = (πh²/9)(dh/dt)

Hence,

     dh/dt = -18/πh² in²/sec

The problems involving related rate exist in many area of engineering research. This table lists most commonly used equations. Their physical meaning will be taught in dynamics and other courses.