Question

The demand x is the number of items that can be sold at a price of $p. For

x = p^3 - 4p + 400,

find the rate of change of p with respect to x by differentiating implicitly.

Answer 1

1 = 3p^2 dp/dx - 4 dp/dx
1 = (3p^2-4) dp/dx
dp/dx = 1/(3p^2-4)

also, note that

dx/dp = 3p^2-4

and dp/dx = 1/(dx/dp)

Answer 2

Answer