Is the following true?
$$\frac{dy}{dx} = \frac{d(y+c)}{dx}$$
where $c$ is an arbitrary real constant.
I believe it is true, and my reasoning goes like this:
$dy$ is an infinitesimal, so the addition of another constant would still be an infinitesimal. I do not know if my reasoning is correct.
Do note that I'm not familiar with epilson delta and university calculus. I would appreciate it if someone could explain the above simply.
EDIT: I couldn't see why $d(y+c)= dy+dc$. What is $d$? Is it a number, or a function?