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May 15th, 2010, 06:38 PM   #1
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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.
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May 15th, 2010, 06:43 PM   #2
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Re: Simplification

it is in its simplest form i think
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May 15th, 2010, 08:30 PM   #3
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Re: Simplification

Hm. I know for a fact that it can be reduced to:

1-1/x^2

..

wulfgarpro.
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May 15th, 2010, 09:03 PM   #4
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Re: Simplification

If I'm not mistaken, I think you simplified incorrectly in your original post.
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May 15th, 2010, 09:03 PM   #5
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Re: Simplification

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May 15th, 2010, 09:06 PM   #6
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Re: Simplification

Yeah, it was the 2 that wasn't cancelled in the original post.
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May 15th, 2010, 09:08 PM   #7
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Re: Simplification

How exactly do the 1/2's and 2 get eliminated ?

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May 15th, 2010, 09:10 PM   #8
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Re: Simplification

2 * 1/2 = 1

x^(1/2) * x^(-1/2) = 1 . . . add the exponents.
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May 15th, 2010, 09:13 PM   #9
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Re: Simplification

I see. I suck at simplifying .. all I can do is practice to get better I guess.

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May 15th, 2010, 09:15 PM   #10
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Re: Simplification

practice practice and practice again . . . that is what I did and it is paying off . . .
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