d(TR)/dQ for the total revenue function TR = 40Q − 3Q √ Q

Question

d(TR)/dQ for the total revenue function TR = 40Q − 3Q √ Q

Answer 1

If TR = 40Q − 3Q√Q then:

TR = 40Q − 3Q•Q^1/2

TR = 40Q − 3Q^3/2

and, by the power rule:

d(TR)/dQ = 40 - (9/2)Q^1/2

or d(TR)/dQ = 40 - (9/2)√Q