What is the rate of change of the volume of a sphere with respect to the radius when the radius is r = 2 in.?

\[V_{sphere} = \frac{4\pi r^3}{3}\]

\[V Prime = 4\pi r^2\]

V Prime = rate of change of sphere

substitute 2 = r for radius, then evaluate

So the answer is 16pi

How did you get V prime? Find the derivative?

Yes

Ok, so when finding the derivative, I would plug (x+h) into r?

Oh you haven't learned the shortcut for taking derivative?

No, not yet.. our teacher is making us do the definition of a derivative.

I'm sorry to hear that

Lol, it's okay, in this case I would put (x+h) into r then, right?

Um, well....hold on

Good luck with using definition of derivative to do this. Your teacher should have shown you how to do it by now.

LOL okay.. thanks though =]

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