Using the Power Rule to Find the Derivative
Date: 9/24/95 at 13:16:7 From: barr Subject: composite functions We are trying to prove that the "power rule" works for finding the derivative of x^(3/2) (where x>0). It has been suggested to us that we first find the derivatives of x^(1/2) and x^3. From here, I assume that we have to utilize the fact that x^(3/2) is the composite of these two functions. However, what is the next step? The rule for the limit of composite functions is sooo confusing! Thanks for your help, Ken.
Date: 9/29/95 at 16:13:43 From: Doctor Andrew Subject: Re: composite functions I started the problem this way: Dx[x^(3/2)] = lim h->0 [(x+h)^(3/2) - x^(3/2)]/h = [(x+h)(x+h)^(1/2) - x(x)^(1/2)] / h I was then able to write the expression as Dx[x^(1/2)] + something else. See if you can do it that way? If you need the next step, just ask. -Doctor Andrew, The Geometry Forum
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