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Find another situation in which you can compose two functions (like area changing with respect to the radius and the radius changing with respect to time). Define variables for each quantity and if applicable write formulas for each relationship. Then describe how the chain rule applies to the situation.
For instance, the perimeter of a square depends on the side length (P = perimeter, s = side length, then P = 4s). If the side length is growing 3 feet per minute (t = times in minutes, s = 3t), how fast is the perimeter growing with respect to time?
Using the chain rule: If s = 3t then ds/dt=3
Now if P = 4s then dp/dt=3
However, we are looking for dp/dt.
So dp/dt=dp/ds ds/dt=4*3=12
Create your own problem and use the chain rule to show how to compute the derivative.
