Calculate related rates in applied contexts. The chain rule is the basis for differentiating variables in a related rates problem with respect to the same independent variable. Other differentiation rules, such as the product rule and the quotient rule, may also be necessary to differentiate all variables with respect to the same independent variable. Interpret related rates in applied contexts. The derivative can be used to solve related rates problems; that is, finding a rate at which one quantity is changing by relating it to other quantities whose rates of change are known.