5. The price of a commodity is *p* dollars and the quantity supplied is *x* units, where

_{}. Find the rate of change of the quantity supplied with respect to time *t* (measured in months) when the price is $4 and is increasing at the rate of 80 cents per month.

**Solution: **Using the chain rule we find that

_{}

From the given equation, and using the Chain Rule again, we find

_{}

Hence,

_{}

But_{}and_{}, which means that

_{}