OK, let's take N items instead of x items.
Let's set N=5 and so f(x)=x+x+x+x+x - that's 5 X's, because N=5.
Let's also completely ignore the value of x for now.

Now let's differentiate f(x); this gives 1+1+1+1+1, which is 5.
We can further simplify f(x)=5x and this differentiates directly to 5, because d/dx (ax^b) = abx^(b-1).

Do you at least agree with that?