Answer
$r^{\prime}(x)=210x^{1.1}$
Work Step by Step
a.
Using the Power and Constant Multiple rules,
$c=100,\quad u(x)=x^{2.1}$
$r^{\prime}(x)=c\cdot u^{\prime}(x)$
$=100\cdot(2.1x^{2.1-1})=210x^{1.1}$
b.
$u(x)=100 ,\ \ \ v(x)=x^{2.1}$
$h(x)=u(x)v(x)$
$u^{\prime}(x)=0,\ \ \ v^{\prime}(x)=2.1x^{1.1}$
Product Rule:
$r^{\prime}(x)=u^{\prime}(x)v(x)+u(x)v^{\prime}(x)$
$= 0(x^{2.1})+100(2.1x^{1.1})=210x^{1.1}$
In both cases (a and b):
$r^{\prime}(x)=210x^{1.1}$
