 Let's have a quick review over the main ideas of section 3.5 in active calculus on related rates. The main concept of this section is that when two or more quantities are related, then the rates at which they change are also related. The problem we are trying to solve here is, given an expression of a relationship between two or more variables, and given information about the rates of change for all but one of those variables, we wish to find the rate of change in the remaining variable. Since rate of change is measured by the derivative, this amounts to just calculating the derivative of a certain quantity, but not in the usual way because that quantity may not be a function, but rather it's just a variable involved in a complex relationship described by an equation. Still, our goal is to calculate the derivative of a quantity at a point given, A, just a relationship between that variable and a few others, and B, the derivatives of the other quantities at that same point. This is best seen through examples, and we have a few of those coming up in addition to the ones in the textbook, but the main workflow for these kinds of problems goes like this, and you should watch to see this workflow instantiated. First, identify the variable whose rate of change you are being asked to find. Second, find an equation that relates that one variable to all the other variables in the problem. This might involve looking up geometry or trigonometry formulas or facts, parsing the language of the problem to convert English expressions into mathematics or something else. Third, all of the variables should have one common input variable, usually that's time. Take the derivative of both sides of the equation that you set up with respect to that one common input variable. You will need to use implicit differentiation in most cases, since the variables here are probably not going to be given as explicit functions of that input variable. Then highlight the rate of change or the derivative that you wanted to find. Then put in all the information for all other quantities in the derivative expression, whether they are derivative values or variable values. You may have to do additional math to get at some of these. Then finally, simply solve for the rate of change you wanted to find. Now let's look at some examples of related rates problems.