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 May 15th, 2010, 06:38 PM #1 Senior Member   Joined: Mar 2010 From: Melbourne Posts: 178 Thanks: 0 Simplification Hi, I have the question: Differentiate: (1/sqrt(x) + sqrt(x))^2 . Using the rule: t/x^y = t*x^-y, I have transformed this function into: (x^(-1/2) + x^(1/2))^2 . Then using the chain rule I have found the derivative to be: 2(x^(-1/2) + x^(1/2))(-1/2x^(-3/2) + 1/2x^(-1/2)) . Simplifying this: 2(x^(-1/2) + x^(1/2))(x^(-3/2) + x^(-1/2)) -- Can this be simplified further ? wulfgarpro.
 May 15th, 2010, 06:43 PM #2 Newbie   Joined: May 2010 Posts: 5 Thanks: 0 Re: Simplification it is in its simplest form i think
 May 15th, 2010, 08:30 PM #3 Senior Member   Joined: Mar 2010 From: Melbourne Posts: 178 Thanks: 0 Re: Simplification Hm. I know for a fact that it can be reduced to: 1-1/x^2 .. wulfgarpro.
 May 15th, 2010, 09:03 PM #4 Senior Member   Joined: Nov 2008 Posts: 265 Thanks: 0 Re: Simplification If I'm not mistaken, I think you simplified incorrectly in your original post.
 May 15th, 2010, 09:03 PM #5 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond Re: Simplification \begin{align*}\frac{d}{dx}\,\left(x^{-1/2}\,+\,x^{1/2}\right)^2\,&=\,2\left(x^{-1/2}\,+\,x^{1/2}\right)\left(-\frac{1}{2}x^{-3/2}\,+\,\frac{1}{2}x^{-1/2}\right) \\ &=\,\left(x^{-1/2}\,+\,x^{1/2}\right)\left(-x^{-3/2}\,+\,x^{-1/2}\right) \\ &=\,-x^{-2}\,+\,x^{-1}\,-\,x^{-1}\,+\,1 \\ &=\,1\,-\,\frac{1}{x^2} \end{align*}
 May 15th, 2010, 09:06 PM #6 Senior Member   Joined: Nov 2008 Posts: 265 Thanks: 0 Re: Simplification Yeah, it was the 2 that wasn't cancelled in the original post.
 May 15th, 2010, 09:08 PM #7 Senior Member   Joined: Mar 2010 From: Melbourne Posts: 178 Thanks: 0 Re: Simplification How exactly do the 1/2's and 2 get eliminated ? wulfgarpro.
 May 15th, 2010, 09:10 PM #8 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond Re: Simplification 2 * 1/2 = 1 x^(1/2) * x^(-1/2) = 1 . . . add the exponents.
 May 15th, 2010, 09:13 PM #9 Senior Member   Joined: Mar 2010 From: Melbourne Posts: 178 Thanks: 0 Re: Simplification I see. I suck at simplifying .. all I can do is practice to get better I guess. wulfgarpro.
 May 15th, 2010, 09:15 PM #10 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond Re: Simplification practice practice and practice again . . . that is what I did and it is paying off . . .

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