# Derivate of Factorial

1. May 13, 2004

### Ebolamonk3y

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

2. May 14, 2004

### fourier jr

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

3. May 14, 2004

### Janitor

4. May 18, 2004

### franznietzsche

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.

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

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

$$x_1-x_0=1$$

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

substituting the general x for

$$x_0$$

and x+1 for

$$x_1$$

we get

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

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