TITLE: Is $\frac{dy}{dx} = \frac{d(y+c)}{dx}$?
QUESTION [5 upvotes]: 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?

REPLY [3 votes]: $$\mathrm{d}(y+c) = \mathrm{d}y + \mathrm{d} c $$
However, if $c$ is a constant, then
$$ \mathrm{d} c = 0 $$
so we get
$$\mathrm{d}(y+c) = \mathrm{d}y$$
Consequently, if one side of the following makes sense, then both sides do and they are equal:
$$\frac{\mathrm{d}(y+c)}{\mathrm{d}x} = \frac{\mathrm{d}y}{\mathrm{d}x}$$