The derivative f'(x) of a function f(x) gives us a way of finding the instantaneous rate of change of that function for any value of x.
Here, we're given the function f(x) = 4x + 7. This function describes a line, and the defining quality of a line is the fact that it has a constant rate of change. This rate of change is described by the slope of the line, which in this case is 4, so we'd say that the rate of change - the derivative - of f(x) for every value of x is 4.
It'll be 4 at x = 1, it'll be 4 at x = 5,and it'll still be 4 at x = 1,000,000