Torture test for convert function

D(p)=74002p+3=7400(2p+3)−1

dDdp=−7400(2p+3)−2(2) (Chain Rule)

=−14800(2p+3)−2

p(t)=5t12+7

dpdt=52t−12

dDdt=dDdpdpdt (Chain Rule)

We want to find the rate of change of demand with respect to time when time t=4.

When t=4  , p(4)=5(4)12+7=5(2)+7=17 , and D(17)=74002(17)+3=740037=200

Also, dpdt|t=4=52(4)−12=1.25 and dDdp|t=4=dDdp|p=17=−14800(37)−2=−10.81

So, the rate of change of demand with respect to time at time t=4 is given by

dDdt|t=4=dDdp|t=4dpdt|t=4

=(−10.81)(1.25)=−13.51

Now, the % rate of change of demand when time t=4  will be given by

(100)(dDdt|t=4)D(p)|t=4=100(−13.51)200=−6.76