Is There a Simple Way to Compute Derivatives for Factorials Beyond the Basics?

[Ebolamonk3y]

Is there a simple neat process to compute derivates for factorials beyond the simple ones...

 

[fourier jr]

I don't understand... can you post the actual problem?

 

[Janitor]

Are you asking about the Gamma function?

If so, this may help:

http://mathworld.wolfram.com/GammaFunction.html

 

[franznietzsche]

Given that the factorial is a discrete function, not a continuous one, there is no continuous derivative, so the discrete derivative is simple to formulate from this basis.

$$<br /> f(x) = x!<br />$$
$$<br /> \frac{df}{dx} = \frac{\delta f}{\delta x}<br /> = \frac{f_1-f_0}{x_1-x_0}<br />$$

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

$$<br /> x_1-x_0=1 <br />$$

$$<br /> \frac{df}{dx} = (x_1)! - (x_0)! <br />$$

substituting the general x for

$$<br /> x_0<br />$$

and x+1 for

$$<br /> x_1 <br />$$

we get

$$<br /> \frac{df}{dx} = (x+1)! - x!<br /> = (x+1)*x! - x!<br />$$
$$= x! * (x+1-1)<br /> = x!*x<br /> = x^2 * (x-1)!<br />$$

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.