Answer
In both cases (a. and b.):
$r^{\prime}(x)=-0.2x^{-2}$
Work Step by Step
a.
Using the Power and Constant Multiple rules,
$c=0.2,\quad u(x)=x^{-1}$
$r^{\prime}(x)=c\cdot u^{\prime}(x)$
$=0.2\cdot(-1x^{-1-1})=-0.2x^{-2}$
b.
$u(x)=0.2 ,\ \ \ v(x)=x^{-1}$
$h(x)=u(x)v(x)$
$u^{\prime}(x)=0,\ \ \ v^{\prime}(x)=-x^{-2}$
Product Rule:
$r^{\prime}(x)=u^{\prime}(x)v(x)+u(x)v^{\prime}(x)$
$= 0(x^{-1})+0.2(-1x^{-1-1})=-0.2x^{-2}$
