Final answer:
The derivative of f(x) = 1/(1-x) can be found using the limit definition of the derivative by calculating the limit of (f(x+h) - f(x))/h as h approaches zero, incorporating knowledge about the function's asymptotic behavior.
Step-by-step explanation:
The question pertains to calculus, specifically dealing with the limit definition of a derivative. The concept involves exploring how the function values change as the inputs get infinitesimally close to a specific point. To find the derivative of the function f(x) = 1/(1-x) using the limit definition, we apply the formula:
lim(h approaches 0) [(f(x+h) - f(x))/h]
This involves calculating the function value at x + h and subtracting the function value at x, then dividing by the interval h, and finally taking the limit as h approaches zero.
Detailed steps for this procedure would involve substituting f(x) = 1/(1-x) into the limit definition and simplifying the resulting expression carefully, taking into account the asymptotic behavior of the function as described by properties such as those outlined by open educational resources like Rice University's OpenStax.