From the given information, we know f'(x) = f(x) and f(1) = 2. Now, consider the function h(x) = f(f(x)).
To find out dh/dx at x = 1, we will have to use the Chain Rule. The Chain Rule states that the derivative of a composition of functions is the derivative of the outer function times the derivative of the inner function. Here, f(x) is the inner function and f(x) is the outer function.
First, we find the derivative of h(x), h'(x), by keeping in mind that in the composition f(f(x)), the outer function is f(u) where u = f(x), and the derivative is f'(u) = f(u). The inner function is u = f(x), and its derivative is u' = f'(x).
Using Chain Rule, h'(x) = f'(f(x))*f'(x). but we know f' = f. So, h'(x) = f(f(x))*f(x).
In order to find the derivative at x = 1, we need to substitute x = 1 into h'(x). Call this value h'(1).
So, h'(1) = f(f(1))*f(1) = f(2)*2.
Given that f(1) = 2, we can sub this in getting h'(1) = f(2)*2. From the equation f'(x) = f(x), so f(2) = 2.
So, h'(1) = 2*2 = 4, which is option B.
The derivative of h with respect to x evaluated at x = 1 is therefore equal to 4. Therefore, the correct answer is B, 4.