Answer
a. Constant Multiple Rule
b. Product Rule: $f^{\prime}(x)=3$ (in both cases)
Work Step by Step
a.
Constant Multiple Rule:$\ \ \ [cf]^{\prime}(x)=cf^{\prime}(x)$
$c=3, \ \ u(x)=x, \ \ $
$f(x)=c\cdot u(x)$
$f^{\prime}(x)=3\cdot u^{\prime}(x)=3(1)=3$
b.
$u(x)=3 ,\ \ \ v(x)=x$
$f(x)=3x=u(x)v(x)$
$u^{\prime}(x)=0,\ \ \ v^{\prime}(x)=1$
Product Rule:
$f^{\prime}(x)=u^{\prime}(x)v(x)+u(x)v^{\prime}(x)=0(x)+3(1)=3$
(the results are equal)