I'm stuck on this problem: write down the four first derivatives of $f(x)= \ln(1+x)$ and hence derive a general expression for the nth derivative of $f$.
The first four derivatives I found are respectively: $$\frac{1}{(1+x)},\; \frac{-1}{(1+x)^2},\;\frac{2}{(1+x)^3},\; \frac{-6}{(1+x)^4}. $$
I know I am missing something simple, but I can't see a pattern… any help would be great!
Best Answer
The sequence $1,1,2,6$ is the sequence $0!, 1!, 2!, 3!$