Suppose $u$ and $v$ are differentiable functions of $x$, and $c$ is a constant. Write down the rules (and verify them) for the following:

(a) $dc$
(b) $d(cu)$
(c) $d(u+v)$
(d) $d(uv)$
(e) $d(u/v)$
(f) $d(x^c)$

*Below, use "du" for $du$, "dv" for $dv$, and "dx" for $dx$.

(a)
(b)
(c)
(d)
(e)
(f)