P = 6(3x + 5)3 − 15

Question

The total physical output P of workers is a function of the number of workers, x. The function P = f(x)

 is called the physical productivity function. Suppose that the physical productivity of x construction workers is given by

P = 6(3x + 5)³ − 15. 

Find the marginal physical productivity, dP/dx. 

dP/dx= ?

Answer 1

Marginal product is the derivative, use the chain rule

P' = 18(3x+5)^2(3) = 54(3x+5)^2