Final answer:
The derivative f'(x) of the function f(x) = x + 1 is 1, as the derivative of x is 1 and the derivative of a constant is 0.
Step-by-step explanation:
The student has asked for the derivative of the function f(x) = x + 1, given that x > 0.
To find f'(x), which represents the derivative of f(x) with respect to x, we apply the basic rules of differentiation.
The derivative of a constant is 0, and the derivative of x with respect to x is 1.
Therefore, the derivative of the function f(x) is simply the coefficient of x, as the constant term (1) disappears during differentiation.