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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 

-Doctor Andrew,  The Geometry Forum
Associated Topics:
High School Calculus

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