Hiya Terry by the step where you list = 18(5000+80t)+4sqrt(5000+80t)+9 , you are on the right track. Since you now have C(t), you can differentiate to find without having to worry about the chain rule with other variables.

The derivative of = 18(5000+80t)+4sqrt(5000+80t)+9 would be = 160*(5000+80t)^(-1/2) + 1440t. C'(2)=160*(5000+80(2))^(-1/2) + 1440(2)

To take the derivative of the square root of 5000+80t a chain rule must be used so

(5000+80t)^(1/2)=

(5000+80t)^(-1/2) * 80 since 80 is the derivate of the inside term.