Derivatives of inverse functions from a table Use the following tables to determine the indicated derivatives or state that the derivative cannot be determined. <IMAGE>
d. f'(1)

Inverse functions are functions that reverse the effect of the original function. If a function f takes an input x and produces an output y, then its inverse f⁻¹ takes y back to x. Understanding how to find and work with inverse functions is crucial for determining derivatives of these functions.

The derivative of an inverse function can be found using the formula (f⁻¹)'(y) = 1 / f'(x), where y = f(x). This relationship shows that the derivative of the inverse at a point is the reciprocal of the derivative of the original function at the corresponding point. This concept is essential for solving problems involving derivatives of inverse functions.

When working with derivatives from a table, it is important to locate the relevant values for the function and its inverse. The table typically provides values of the function and its derivative at specific points, which can be used to find the derivative of the inverse function. If the necessary values are not present, it may be impossible to determine the derivative.