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: 11/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 
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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