Find the nnn-th derivative formula for f(x)=11−xf(x) = \frac{1}{1-x}f(x)=1−x1 (for ∣x∣<1|x|<1∣x∣<1).
n!(1−x)n+1\frac{n!}{(1-x)^{n+1}}(1−x)n+1n!
(−1)nn!(1−x)n+1\frac{(-1)^n n!}{(1-x)^{n+1}}(1−x)n+1(−1)nn!
n!(1+x)n+1\frac{n!}{(1+x)^{n+1}}(1+x)n+1n!
1(1−x)n+1\frac{1}{(1-x)^{n+1}}(1−x)n+11