A product is introduced to the market. The weekly profit (in dollars) of that product decays exponentially as function of the price that is charged (in dollars) and is given by $\displaystyle {P}{\left({x}\right)}={65000}\cdot{e}^{{-{0.04}\cdot{x}}}$

Suppose the price in dollars of that product, $\displaystyle {x}{\left({t}\right)}$, changes over time $\displaystyle {t}$ (in weeks) as given by $\displaystyle {x}{\left({t}\right)}={36}+{0.95}\cdot{t}^{{2}}$

Find the rate that profit changes as a function of time, $\displaystyle {P}'{\left({t}\right)}$ Preview Question 6 Part 1 of 2   dollars/week

How fast is profit changing with respect to time 6 weeks after the introduction. Preview Question 6 Part 2 of 2   dollars/week