Consider this function:
$$f(x) = 2x +1$$
it can be seen as a composite function: $f(g(x))$ with
$$f(x) = x + 1$$ $$g(x) = 2x$$
Using the chain-rule to derive the original $f(x)$ I got:
$$f'(x) = d(2x + 1) \cdot 2 $$
Denoting with $d(\cdot)$ the derivative operation respect to $x$
But then solving $d(2x + 1)$ simply distributing derivative operator over sum I got:
$$f'(x) = 2 \cdot 2 = 4$$
Which is wrong.
What is my mistake? What I was getting wrong?
I can't consider $f(x)$ as a composite function?