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# Applying the chain rule in 'rate of change' type questions watch

1. Hi i came accross a question before that has really stumped me!

Water is poured on a surfrace.It forms a circular patch which is growing at a steady rate of 5cm^2 /s, find in terms of pi

1)the radius of the patch 20 seconds after pourign has commenced
2)the rate of increase of the radius at this instant.

im quite good with this stuff tbh so i know how i should be going about working it out, just not gettin anywhere today!

2. Differentiate wrt time
3. The question is telling you 2 things:

(The area is increasing by 5 every second)

(It's forming a circle)

Now try applying the chain rule...
4. ... given that you want dr/dt for the first part. For the second part, you need to find an expression for the area of the circle as a function of time.
5. have you come across differential equations cos that is exactly what this is
6. also remember to use that (this is jus an e.g)

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Updated: September 23, 2008
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