Explanation Given Information: The provided equation of the curve is, y 2 ln x + x 2 y = 3 and point is ( 1 , 3 ) . Formula used: The slope of tangent to a curve y = f ( x ) at point ( x , y ) is given by the derivative of the curve at that point. According to the product rule of derivatives, d d x ( u ⋅ v ) = u d v d x + v d u d x Calculation: Consider the provided equation of curve, y 2 ln x + x 2 y = 3 Now, find the derivative d y d x from y 2 ln x + x 2 y = 3 by taking the derivative term by term on both sides of the equation as, d d x ( y 2 ln x ) + d d x ( x 2 y ) = d d x ( 3 ) Now, use the product rule, d d x ( u ⋅ v ) = u d v d x + v d u d x To obtain the derivative of y 2 ln x and x 2 y as, y 2 d d x ( ln x ) + ln x d d x ( y 2 ) + y d d x

Mathematical Applications for the Management, Life, and Social Sciences

12th Edition

ISBN: 9781337625340

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

See similar textbooks

Videos

Question

Chapter 11.3, Problem 41E

To determine

To calculate: The slope of the tangent line to the curve y2lnx+x2y=3 at (1,3).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.3, Problem 40E

Chapter 11.3, Problem 42E

Students have asked these similar questions

Why the correct answer is letter A? Students in an online course are each randomly assigned to receive either standard practice exercises or adaptivepractice exercises. For the adaptive practice exercises, the next question asked is determined by whether the studentgot the previous question correct. The teacher of the course wants to determine whether there is a differencebetween the two practice exercise types by comparing the proportion of students who pass the course from eachgroup. The teacher plans to test the null hypothesis that versus the alternative hypothesis , whererepresents the proportion of students who would pass the course using standard practice exercises andrepresents the proportion of students who would pass the course using adaptive practice exercises.The teacher knows that the percent confidence interval for the difference in proportion of students passing thecourse for the two practice exercise types (standard minus adaptive) is and the percent…

3. A spring is stretched 6 in. by a mass that weighs 8 lb. The mass is attached to a dashpot mechanism that has a damping constant of 0.25 lb-sec./ft. and is acted on by an external force of 4 cos 2t lb. a. Set-up the differential equation and initial value problem for the system. b. Write the function in phase-amplitude form. C. Determine the transient solution to the system. Show your work. d. Determine the steady state of this system. Show your work. e. Is the system underdamped, overdamped or critically damped? Explain what this means for the system.

4. Suppose that you have a circuit with a resistance of 20, inductance of 14 H and a capacitance of 11 F. An EMF with equation of E(t) = 6 cos 4t supplies a continuous charge 60 to the circuit. Suppose that the q(0)= 8 V and the q'(0)=7. Use this information to answer the following questions a. Find the function that models the charge of this circuit. b. Is the circuit underdamped, overdamped or critically damped?

Chapter 11 Solutions

Mathematical Applications for the Management, Life, and Social Sciences

Ch. 11.1 - 1. Ch. 11.1 - 2. If Ch. 11.1 - Prob. 3CP Ch. 11.1 - 4. Find . Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Find the derivatives of the functions in Problems...

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 slope of the tangent line to the curve y 2 ln x + x 2 y = 3 at ( 1 , 3 ) .

Solution Summary: The author explains the formula used to calculate the slope of the tangent line to a curve.

Videos

To calculate: The slope of the tangent line to the curve y2lnx+x2y=3 at (1,3).

Want to see the full answer?

Chapter 11 Solutions