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Derivate of x^p

  1. Oct 8, 2004 #1
    Let y = x^p where p is a natural number. Is it true that
    [tex] \frac{dx^n}{d^ny} = \frac{p!}{(p-n)!} \cdot x^{p-n} [/tex] with the restriction that we define [tex] (-n)! \equiv \infty [/tex] for n=1,2,3... I found this formula and I believe that it is true if we define [tex] (-n)! [/tex] to equal [tex] \infty [/tex].
     
  2. jcsd
  3. Oct 8, 2004 #2

    mathman

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    Science Advisor

    Your answer is correct, although you wrote the derivative upside down. The definition you used for (-n)! is the standard one.
     
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