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More on finding the nth derivative

  1. Sep 30, 2007 #1
    I have another question on finding the nth derivative. Is there a set formula i can follow for finding the nth derivative of different functions or do i need to find different patterns in order to come up with a formula each time.

    I also need to find formulas for the nth derivative of:
    f(x)= x^n

    f(x)= 1/ (3x^3)

    f(x)= square root of x

    Does anyone know how these formulas or an easy way of coming up with them?
  2. jcsd
  3. Sep 30, 2007 #2
    It's a guess. But for x^n it should be pretty easy -- a bit of induction should sort it out, and the other two are just a special cases.
  4. Sep 30, 2007 #3


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    Only way I know how to get the nth derivative is to just differentiate about 3 times and hope to see a pattern
  5. Sep 30, 2007 #4


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    As genneth and rock.freak667 point out, the trickiest thing here is that there are different cases to consider. Try different starting values for n (remember, n can be any real number) and see what happens...

    As with your other thread, it will make things easier if you start from

    (3x^3)^(-1) and x^(1/2) .
  6. Sep 30, 2007 #5


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    for the nth derivative of [tex]x^n[/tex] try differentiating that about 4 times and try to deduce the 5th derivative

    (hint: n(n-1)(n-2)(n-3)(n-4)(...)=n!)
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