Explanation Given: The function is f ( x , y ) = x ln ( x y ) . To obtain the value of f x x ( x , y ) , find the partial derivative of the function with respect to x . That is, treating y as a constant differentiate the function with respect to x . f x ( x , y ) = ∂ ∂ x ( x ln ( x y ) ) = ( x ) ∂ ∂ x ( ln ( x y ) ) + ( ln ( x y ) ) ∂ ∂ x ( x ) = ( x ) ( ∂ ∂ ( x y ) ( ln ( x y ) ) ∂ ∂ x ( x y ) ) + ( ln ( x y ) ) ∂ ∂ x ( x ) Simplify further and obtain the partial derivative. f x ( x , y ) = ( x ) ( 1 x y ( y ) ) + ( ln ( x y ) ) ( 1 ) = 1 + ln ( x y ) Therefore, the partial derivative of the function with respect to x is f x ( x , y ) = 1 + ln ( x y ) . Find the partial derivative of f x ( x , y ) = 1 + ln ( x y ) with respect to x . f x x ( x , y ) = ∂ ∂ x ( 1 + ln ( x y ) ) = ∂ ∂ x ( 1 ) + ∂ ∂ x ( ln ( x y ) ) = 0 + ∂ ∂ ( x y ) ( ln ( x y ) ) ∂ ∂ x ( x y ) Simplify further and obtain the partial derivative. f x x ( x , y ) = 1 x y ( y ) = 1 x Therefore, the second order partial derivative f x x ( x , y ) = 1 x . Now, obtain the value of f x y ( x , y ) . To find the partial derivative f x y ( x , y ) = ∂ ∂ y ( ∂ f ∂ x ) , substitute f x ( x , y ) = 1 + ln ( x y ) in f x y ( x , y ) = ∂ ∂ y ( ∂ f ∂ x ) . f x y ( x , y ) = ∂ ∂ y ( 1 + ln ( x y ) ) = ∂ ∂ y ( 1 ) + ∂ ∂ y ( ln ( x y ) ) = 0 + ∂ ∂ ( x y ) ( ln ( x y ) ) ∂ ∂ y ( x y ) Simplify further and obtain the partial derivative

Pearson eText for College Mathematics for Business, Economics, Life Sciences, and Social Sciences -- Instant Access (Pearson+)

14th Edition

ISBN: 9780137553341

Author: Raymond Barnett, Michael Ziegler

Publisher: PEARSON+

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 14.2, Problem 74E

To determine

To find: The second order partial derivatives fxx(x,y), fxy(x,y), fyz(x,y) and fyy(x,y).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.2, Problem 73E

Chapter 14.2, Problem 75E

Students have asked these similar questions

1. Consider the following preference ballots: Number of voters Rankings 6 5 4 2 1st choice A DCB DC 2nd choice B B D 3rd choice DCBD 4th choice CA AAA For each of the four voting systems we have studied, determine who would win the election in each case. (Remember: For plurality with runoff, all but the top two vote-getters are simultaneously eliminated at the end of round 1.)

Practice k Help ises A 96 Anewer The probability that you get a sum of at least 10 is Determine the number of ways that the specified event can occur when two number cubes are rolled. 1. Getting a sum of 9 or 10 3. Getting a sum less than 5 2. Getting a sum of 6 or 7 4. Getting a sum that is odd Tell whether you would use the addition principle or the multiplication principle to determine the total number of possible outcomes for the situation described. 5. Rolling three number cubes 6. Getting a sum of 10 or 12 after rolling three number cubes A set of playing cards contains four groups of cards designated by color (black, red, yellow, and green) with cards numbered from 1 to 14 in each group. Determine the number of ways that the specified event can occur when a card is drawn from the set. 7. Drawing a 13 or 14 9. Drawing a number less than 4 8. Drawing a yellow or green card 10. Drawing a black, red, or green car The spinner is divided into equal parts. Find the specified…

Problem 1.We consider a two-period binomial model with the following properties: each period lastsone (1) year and the current stock price is S0 = 4. On each period, the stock price doubleswhen it moves up and is reduced by half when it moves down. The annual interest rateon the money market is 25%. We consider four options on this market: A European call option with maturity T = 2 years and strike price K = 5; A European put option with maturity T = 2 years and strike price K = 5; An American call option with maturity T = 2 years and strike price K = 5; An American put option with maturity T = 2 years and strike price K = 5.(a) Find the price at time 0 of both European options.(b) Find the price at time 0 of both American options. Compare your results with (a)and comment.(c) For each of the American options, describe the optimal exercising strategy.(d) We assume that you sell the American put to a market participant A for the pricefound in (b). Explain how you act on the market…

Chapter 14 Solutions

Pearson eText for College Mathematics for Business, Economics, Life Sciences, and Social Sciences -- Instant Access (Pearson+)

Ch. 14.1 - Matched Problem 1 Find C(20, 10) for the cost...Ch. 14.1 - Prob. 2MP Ch. 14.1 - Prob. 3MP Ch. 14.1 - Prob. 4MP Ch. 14.1 - Prob. 5MP Ch. 14.1 - Prob. 6MP Ch. 14.1 - Prob. 7MP Ch. 14.1 - Prob. 1ED Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The second order partial derivatives f x x ( x , y ) , f x y ( x , y ) , f y z ( x , y ) and f y y ( x , y ) .

Concept explainers

Videos

To find: The second order partial derivatives fxx(x,y), fxy(x,y), fyz(x,y) and fyy(x,y).

Want to see the full answer?

Chapter 14 Solutions