Related Rates Calculus?

Answer 1

Related rates: The important use of the Chain rule is to find the rates of change of two or more related variables that are changing with respect to time.

For example, when water is drained out of a conical tank, the volume V, the radius r, and the height h of the water level are all functions of time t. We know that these variables are related by the equation V = (π/3)r²h.

Differentiate implicitly with respect to t to obtain the related-rate equation

(d/dt)(V) = (d/dt)[(π/3)r²h]

V' = (π/3)[r²h' + 2rhr']

From the above equation we can see that the rate of change of V is related to the rates of change of both h and r.