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Math Help - Calculating the fifth derivative

  1. #1
    Senior Member Paze's Avatar
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    Calculating the fifth derivative

    So I've got this problem:

    Calculate the fifth derivative of the function f(x)=xe^x

    I tried going through the hassle of doing product rule again and again but it became so messy by the third iteration that I have to believe that there is an easier way to solve this problem (and perhaps other problems like it?).

    Thanks.
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  2. #2
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    Re: Calculating the fifth derivative

    Hey Paze.

    The way you are doing it is the way to do it (and yes it will probably be very messy).
    Thanks from Paze
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  3. #3
    Senior Member Paze's Avatar
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    Re: Calculating the fifth derivative

    Oh, I see. Thanks!
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  4. #4
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    Re: Calculating the fifth derivative

    Actually, not all that messy.....

    - Hollywood
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    Senior Member Paze's Avatar
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    Re: Calculating the fifth derivative

    Quote Originally Posted by hollywood View Post
    Actually, not all that messy.....

    - Hollywood
    Care to explain? It becomes pretty messy for me.
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  6. #6
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    Re: Calculating the fifth derivative

    If you apply the product rule to (x+n)e^x, you get (x+n)(e^x)'+(x+n)'(e^x) = (x+n)e^x + e^x = (x+n+1)e^x. So if you start with (x+0)e^x and apply it 5 times, you get (x+5)e^x.

    - Hollywood
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  7. #7
    Senior Member Paze's Avatar
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    Re: Calculating the fifth derivative

    Quote Originally Posted by hollywood View Post
    If you apply the product rule to (x+n)e^x, you get (x+n)(e^x)'+(x+n)'(e^x) = (x+n)e^x + e^x = (x+n+1)e^x. So if you start with (x+0)e^x and apply it 5 times, you get (x+5)e^x.

    - Hollywood
    Where does that n come from? I just did product rule on xe^x and somehow, natural logarithms started getting mixed and what not..
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  8. #8
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    Re: Calculating the fifth derivative

    n is any integer.

    So when you take the first derivative, you get xe^x+e^x. You can write that (x+1)e^x. Now try taking the derivative again.

    - Hollywood
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  9. #9
    Senior Member Paze's Avatar
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    Re: Calculating the fifth derivative

    Ah, I see. Thanks.
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  10. #10
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    Re: Calculating the fifth derivative

    its easy the nth derivative of xe^x is e^x[x+n] as simple as such.
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