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

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Chapter 11.3, Problem 41E

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

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Chapter 11.3, Problem 40E

Chapter 11.3, Problem 42E

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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...

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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.

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

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Chapter 11 Solutions