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Derivate of Factorial

  1. May 13, 2004 #1
    Is there a simple neat process to compute derivates for factorials beyond the simple ones...
     
  2. jcsd
  3. May 14, 2004 #2
    I don't understand... can you post the actual problem?
     
  4. May 14, 2004 #3

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  5. May 18, 2004 #4
    Given that the factorial is a discrete function, not a continuous one, there is no continous derivative, so the discrete derivative is simple to formulate from this basis.

    [tex]

    f(x) = x!

    [/tex]
    [tex]

    \frac{df}{dx} = \frac{\delta f}{\delta x}
    = \frac{f_1-f_0}{x_1-x_0}

    [/tex]

    Now because f(x) is discrete, the only important values are integers so

    [tex]

    x_1-x_0=1

    [/tex]

    [tex]

    \frac{df}{dx} = (x_1)! - (x_0)!

    [/tex]

    substituting the general x for

    [tex]

    x_0

    [/tex]

    and x+1 for

    [tex]

    x_1

    [/tex]

    we get

    [tex]

    \frac{df}{dx} = (x+1)! - x!
    = (x+1)*x! - x!

    [/tex]
    [tex]
    = x! * (x+1-1)
    = x!*x
    = x^2 * (x-1)!

    [/tex]

    There is your discrete derivative for integer values of x, it is the difference between the value of f at x and x+1 in terms of x.


    Note: LaTeX friggin hates me.
     
    Last edited: May 18, 2004
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