what is the equation for the n derivative of ln(x) $ y=ln(x) $  then  i must find  $ y^{(n)}  $ for $ n= Naturals $
i found that the general formula is  
$ y^{(n)}= \frac{(n-1)!}{x^n} $ when n is an odd number
and 
$ y^{(n)}= -\frac{(n-1)!}{x^n} $ when n is an even number 
so i would like to make this into one equation but i can't think of any function that works as desired (changing from -1 to 1 in every natural) maybe floor ceiling of sine or cosine

Throw in a $(-1)^n$, or $(-1)^{n+1}$, depending on the parity.
By the way, there's nothing wrong with having different forms for the even and odd natural numbers.
