Final answer:
To find the derivative of the inverse function (f^-1)'(a), we use the relationship 1 / (f'(f^-1(a))). Without specific details about the function f, however, we cannot calculate the derivative of its inverse at a specific value.
Step-by-step explanation:
To find (f-1)'(a), we need to consider the function f and its inverse. According to the discussion provided, we have a situation where the product of f and some quantity is a constant, indicating we might be dealing with an inverse function or a reciprocal relationship. Though the given information is fragmented, one approach is to use the derivative of the inverse function, which is 1 / (f'(f-1(a))). However, if we lack more specific information about the function f, we cannot compute this derivative exactly.
In the context of the provided excerpts, it seems there is an allusion to the relationship between f and its inverse as well as concepts involving squares and square roots, as seen in the discussion about inverting the square of a side of a triangle to find the side length itself. This illustrates the general principle of inverting a function to undo an operation. Therefore, if f can be identified and its derivative f' is known, we can compute the derivative of f's inverse at a by applying the formula above.