Given f(x)=xx+1f(x) = \frac{x}{x+1}f(x)=x+1x, find f(n)(x)f^{(n)}(x)f(n)(x).
n!(x+1)−(n+1)n!(x+1)^{-(n+1)}n!(x+1)−(n+1)
(−1)nn!(x+1)−(n+1)(-1)^n n!(x+1)^{-(n+1)}(−1)nn!(x+1)−(n+1)
(−1)n+1n!(x+1)−(n+1)(-1)^{n+1} n!(x+1)^{-(n+1)}(−1)n+1n!(x+1)−(n+1)
n!(x+1)−nn!(x+1)^{-n}n!(x+1)−n