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Differentiation of fractional and negative powers

  1. Jan 19, 2005 #1
    hello reader

    i have a problem understanding the following type of equation.

    (n+x)/nth root of x

    n being a fixed numerical value and x being the unknown

    how would i differentiate such a problem

    an example of this is:

    (1+x)/4th root x
    thank you
     
  2. jcsd
  3. Jan 19, 2005 #2

    dextercioby

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    U mean this

    [tex] (x^{\frac{1}{4}})'=...? [/tex]

    If so,apply the rule for differentiating any power of "x"...

    Daniel.
     
  4. Jan 19, 2005 #3
    the question reads 1+x/4th root of x

    therefore to simplify this:

    (1+x) divided by (x^1/4)

    how do i get this fraction in to a negative function of x

    if this was 1 divided by 4th root of x i know that this is then 1/x^1/4
    which is x^-1/4

    however, when there is a '+x' involved, i get stuck. what do you do with the 1+x to differentiate
     
  5. Jan 19, 2005 #4

    dextercioby

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    Aaa,that's something else.

    [tex] [\frac{1+x}{x^{\frac{1}{4}}}]'=[x^{-\frac{1}{4}}(1+x)]' [/tex]

    Now differentiate like a product...

    Daniel.
     
  6. Jan 19, 2005 #5

    HallsofIvy

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    Or,and I think simpler, write [itex]x^{-\frac{1}{4}}(1+x)= x^{-\frac{1}{4}}+ x^{\frac{3}{4}}[/itex] and differentiate that.
     
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