What are the Related Rates?Suppose that two variables x and y are functions of a variable, t:Thenandare the rates of change of x and y with respect to t.
Sometimes x and y are related by means of an equation, such as:Differentiate implicitly with respect to t:The derivativesare called related rates since they’re related by meansof an equation.●We can findifis given and vice versa.
Example 1How fast does the radius of a spherical soap bubble change at the moment whenthe radius is 1 cm if the air is blown into it at the rate of 10 cm3/sec?How to solve problems of this kind? You should follow the 7 steps as below:
1.Draw diagram (if needed)2.Write down what is given andwhat is asked for3.Write the equation that relatesthe variables4.Implicitly differentiate5.Plug in given values6.Find values that are not directlygiven and plug them in as well(if needed)7.Find the unknownVsphere= 4/3 pi R31 dV/dt = 4 pi R2dR/dtGiven:
Example 2How fast does the water level drop when a cylindrical tank with a radius of 1 m is