Taylor expansion for Logistic function near a point different than zero

Question

How to derive Taylor series expansion for Logistic function near a point $x=a\neq0$ of the form:

$$L(x) = \frac{1}{1+e^{-k(x-x_0)}}$$

Edit

Using the general form for Taylor series coefficients $c_n=\frac{f^{(n)}(x_0)}{n!}$

I couldn't find a general form for the derivative of L, because each derivative degree has it's own formula.