Final answer:
To find the nth derivative of f(x) = (x+1)^-1, apply the power rule and chain rule. The nth derivative is (-1)^n * n!(x+1)^-(n+1).
Step-by-step explanation:
The nth derivative of the function f(x) = (x+1)^-1 can be found using the power rule and the chain rule.
Let's find the first few derivatives to establish a pattern. The first derivative is found by using the power rule: (x+1)^-2.
The second derivative can be found by applying the power rule again: -2(x+1)^-3. The third derivative would be: 2*3(x+1)^-4.
From these derivatives, we can see that the coefficient in front of each derivative is equal to n! (the factorial of n). Therefore, the nth derivative of f(x) = (x+1)^-1 is (-1)^n * n!(x+1)^-(n+1).