## Finite Math and Applied Calculus (6th Edition)

$r^{\prime}(x)=210x^{1.1}$
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): $r^{\prime}(x)=210x^{1.1}$