Example CCD.DSUM: The derivative of sums of functions: The Sum Rule.
Suppose $f$ and $g$ are differentiable functions ( at $x=a$) and $S=f+g$ or $S=f-g$.
Then $S$ is also differentiable ( at $x=a$) and

$D_x (f +g)(a) = D_x f(a) +D_x g(a)$ or $\frac {d (f +g)}{dx}|_{x=a} = \frac {d f}{dx}|_{x=a}+\frac {dg}{dx|_{x=a}}$

$D_x (f -g)(a) = D_x f(a) - D_x g(a)$ or $\frac {d (f -g)}{dx}|_{x=a} = \frac {d f}{dx}|_{x=a}-\frac {dg}{dx|_{x=a}}$