Question

Suppose that the supply of x units of a product at price p dollars per unit is given by the following. P=20+90ln(7x+8)

Find the rate of change of supply price with respect to the number of units supplied. dp/dx=

Answer 1

To find the rate of change of the supply price with respect to the number of units supplied, we can use the chain rule to find the derivative of the supply function with respect to x.

Step-by-step explanation:

To find the rate of change of the supply price with respect to the number of units supplied, we need to find the derivative of the supply function with respect to x. The supply function is given as P = 20 + 90ln(7x+8). To find dp/dx, the derivative of P with respect to x, we can use the chain rule:

dp/dx = dP/dx = (dP/d(7x+8)) * (d(7x+8)/dx) = 90 * (7/(7x+8)).

Therefore, the rate of change of the supply price with respect to the number of units supplied is 90 * (7/(7x+8)).