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Induction proof of nth derivative

  1. Sep 22, 2008 #1
    Show by induction that the nth derivative f(n)(x) of;

    f(x)=sqrt(1-x)

    is

    f(n)(x)= -[tex]\frac{(2n)!}{4^{n}n!(2n-1)}[/tex]*(1-x)(1/2)-n

    for n [tex]\geq[/tex] 1.
     
  2. jcsd
  3. Sep 22, 2008 #2
    For n=1 it works.

    For n=k-1 assume that it works. Write n=kth derivative as the derivative of the expression for k-1, i.e d(f(k-1)(x))/(dx). Taking the derivative the result follows.
     
  4. Sep 22, 2008 #3

    Redbelly98

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    Homework questions should be posted in the homework section of this forum.

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