Final answer:
The nth derivative of 1/x can be found using the power rule for differentiation.
Step-by-step explanation:
The nth derivative of 1/x can be found using the power rule for differentiation. The power rule states that if you have a function f(x) = x^n, then the nth derivative of f(x) is given by:
f(n)(x) = n(n-1)(n-2)...(n-(n-1))x^(n-n)
For 1/x, the function can be rewritten as x^(-1). Applying the power rule, we get:
f'(x) = (-1)(-1 - 1)x^(-1 - 2) = 2x^(-3)
So, the nth derivative of 1/x is given by f(n)(x) = n!x^(-n-1).