Exam 3: Shortcuts to Differentiation

The derivative of is .

Find the first derivative of .

If , then = .

The concentration, in , of a drug introduced gradually into the body can be modeled by minutes. At what time does the concentration reach its maximum?

Is the derivative of given by ?

A demand curve for a product has the equation , where p is price and q is quantity. What is the marginal revenue as a function of the quantity sold?

The first derivative of is

With a yearly inflation rate of 3%, prices are described by , where is the price in dollars when t = 0 and t is time in years. If = 1.2, how many cents per year are prices rising when t = 12? Round to the nearest tenth of a cent.

The price in dollars of a house during a period of mild inflation is described by the formula , where t is the number of years after 1990. By how many dollars per year will the value of the house be increasing in the year 2015? Round to the nearest dollar.

Given and , find .

Given the following table, let . Find .

The following table gives values for two functions f and g and their derivatives. What is ?

Given , find .

Differentiate .

Differentiating gives .

Given , , and , what is ?

Find the first derivative of w = x² + ax.

Find if

Find the first derivative of .

If $100 is invested at r % interest per year, compounded yearly, then the yield after 15 years is given by . Find .