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Simple Derivitive

  1. Jul 13, 2005 #1
    How do I deal with the square root in [itex]y = \sqrt{x}(x - 1)[/itex]?
  2. jcsd
  3. Jul 13, 2005 #2
    [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]
  4. Jul 13, 2005 #3
    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).
    Last edited: Jul 13, 2005
  5. Jul 13, 2005 #4
    Can I get any further that here?

    [tex]\left(x - 1\right)\left(\frac{1}{2\sqrt{x}}\right) + \sqrt{x}[/tex]
    Last edited: Jul 13, 2005
  6. Jul 13, 2005 #5
    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.
    Last edited: Jul 13, 2005
  7. Jul 13, 2005 #6
    [tex]1\frac{1}{2}x^{\frac{1}{2}} - \frac{1}{2}x^{-\frac{1}{2}}[/tex]

  8. Jul 13, 2005 #7
    First part is incorrect, second part is correct.
  9. Jul 13, 2005 #8
    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]?
  10. Jul 13, 2005 #9
    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?
    Last edited: Jul 13, 2005
  11. Jul 13, 2005 #10
    Thanks for the tip and your help (Berislav too) :smile:
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