Final answer:
The question seeks the derivative h'(1) for h(x) = f[f(x)]. To calculate it, we need the chain rule and values from f and f' at specific points, which are not provided.
Step-by-step explanation:
The question asks for the derivative of the function h(x), which is defined as f[f(x)]. To find h'(1), also known as the derivative of h at x=1, we would apply the chain rule. However, there is insufficient data provided in the question details. Normally, we would need the values of f and f' at relevant points, derived from a given table, to use the chain rule effectively. If the necessary values were given, we would find f'(f(1)) and multiply it by f'(1) to obtain h'(1). f' indicates the derivative of the function f. The lack of this information prevents us from calculating the precise value of h'(1).