Exam 3: Shortcuts to Differentiation

If , then = .

The first derivative of is .

What is the equation of the tangent line to at the point where x = 0?

Find the first several derivatives of , where a is a constant. Use them to predict the 15^th derivative of .

The first derivative of is .

is equivalent to

Differentiating gives .

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. How many years will it be before the house in increasing in value at a rate of $15,000 per year? Round to the nearest year.

If and , then which two of the following are and ?

When , the graph of is

The equation for the tangent line to the function at x = 1 is y = _____x + _____.

Differentiating gives .

Find the derivative of . A) B) C) D)

The first derivative of is .

The equation of the tangent line to the graph of at the point at which x = 0 is y = _____ _____. Enter fractions in the form "a/b".

Find the equation of the tangent line to the graph of at (round to two decimal places).

Find the derivative of .

The population of Ghostport has been declining since the beginning of 1800. The population, in thousands, is modeled by , where t is measured in years. At what rate was the population declining at the beginning of 2000?

The equation for the tangent line to the curve when x = 3 is y = _____x + _____.

Consider the function . We know that is increasing when x > _____.