Given a total$-$revenue function $R(x)=900\sqrt[\phantom{2}]{x^2-0\mathrm{.}2x}$ and a total$-cost$ function $C(x)=2000(x^2+5{)}^{\frac{1}{3}}+600,$ both $in$ thousands $of$ dollars, find the rate $at$ which total profit $is$ changing when $x$ items have

been produced and sold.

$P^{\text{'}}(x)=$