Question

Assume that the profit generated by a product is given by p(x) = 3√x where x is the number of units sold. If the profit keeps changing at a rate of $900 per month, then how fast are the sales changing when the number of units sold is 400?

Answer 1

Check the explanation

Explanation:

Using the chain rule: dp/dx=(dp/dt)/(dx/dt).

So, you can calculate dp/dx=2x^(-1/2)=2/√x.

by my original statement (rearranged a little) dx/dt (which is what you're looking for) is equal to (dp/dt)/(dp/dx), so subbing in x=1900 you get 1000√1900/2=21794.495 units/month increase in sales.