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Prove the case r= -n (n is a positive integer)of the general power rule

  1. Oct 3, 2012 #1
    Prove that:
    d/dx x^-n = -nx^-n-1
    Use the factorization of a difference of nth powers given in this section (not using quotient rule)
    My attempt gets me from the definition of the derivative to (1/n^(n-1)) n times... I need the negative. I get nx^(-n-1) instead of -nx^(n-1).
     
  2. jcsd
  3. Oct 3, 2012 #2

    HallsofIvy

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    Since you chose not to say what "the factorization of a difference of nth powers given in this section" nor now you attempted to do this, I don't see how you can expect any one to help.

    Since you are not allowed to use the quotient rule, I would recommend writing [itex]x^n(x^{-n})= 1[/itex] and differentiating both sides, using the product rule on the left. What do you get when you do that?
     
    Last edited: Oct 3, 2012
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