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Related rates - Derivative Applications

Related rates

Related rates come in handy when we have two related quantities and one of their rates of change is much harder to find than the other one. For example, look at the figure below, you can see that it is difficult to find the rate of change in radius of the balloon while it is being pumped up. However, the rate of change in volume of the balloon can be easily found if we know the air flow rate of the pump. Therefore, the work left with us is just to find the equation that relates the two related quantities, and then use the Chain Rule to differentiate both sides with respect to time.



Note: Problem Solving Strategy
1. If possible, draw a diagram to help visualize the problem.
2. Express the given rates (look for units with time in the denominator).
3. Express the asking rate (look for phrases such as “how fast”, “at what rate”, “find the rate”, etc.).
4. Write an equation that relates the various quantities of the problem.
5. Differentiate both sides of the equation, with respect to time, using the Chain Rule.
6. Substitute the given information into the differential equation and solve for the asking rate.
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Related rates

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