Simple Derivitive

  • Thread starter cscott
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  • #1
782
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How do I deal with the square root in [itex]y = \sqrt{x}(x - 1)[/itex]?
 

Answers and Replies

  • #2
789
4
[tex]\sqrt{x} = x^{(\frac{1}{2})}[/tex]

Distribute and take it away.

Also, remember that [tex]a^x*a^y=a^{(x+y)}[/tex]
 
  • #3
238
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You know the simple formula for deriving powers of x, right? Well, [itex] \sqrt{x}=x^{\frac{1}{2}}[/itex]

EDIT: I was slow. Sorry, I didn't mean chain, I meant distrubution for derivation (didn't know what you call it in English).
 
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  • #4
782
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Can I get any further that here?

[tex]\left(x - 1\right)\left(\frac{1}{2\sqrt{x}}\right) + \sqrt{x}[/tex]
 
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  • #5
789
4
You're making it more complicated than neccessary.

Distribute the [itex]\sqrt{x}[/itex] then take the derivative.

Ok, your way works, but I wouldn't do it that way. That's the beauty of it though, many correct ways to get the same answer.
 
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  • #6
782
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[tex]1\frac{1}{2}x^{\frac{1}{2}} - \frac{1}{2}x^{-\frac{1}{2}}[/tex]

correct?
 
  • #7
789
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First part is incorrect, second part is correct.
 
  • #8
782
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Hmm I don't see how :frown:

[itex]x^{\frac{1}{2}} \cdot x^1 = x^{1.5}[/itex] so doesn't that become [itex]1.5 \cdot x^{\frac{1}{2}}[/itex]?
 
  • #9
789
4
Oh, ok. You were righting a mixed fraction. It would be best to write 1.5 as [itex]\frac{3}{2}[/itex]

Try not to use mixed fractions, they get too confusing. Use improper ones.

For example: take the derivative of [tex]3\frac{1}{2}\frac{5}{7}x^4[/tex] with respect to x. Make sense?
 
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  • #10
782
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Jameson said:
Oh, ok. You were righting a mixed fraction. It would be best to call 1.5 [tex]\frac{3}{2}[/tex]

Try not to use mixed fractions, they get too confusion. Use improper ones.
Thanks for the tip and your help (Berislav too) :smile:
 

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