Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Section 3.5 - Implicit Differentiation - 3.5 Exercises: 23

Answer

$dx/dy=\frac{2x^4y-x^3+6xy^2}{4x^3y^2-3x^2y+2y^3}$

Work Step by Step

Take the derivative as is on either side of the equation: $2x^4y+4x^3y^2(dx/dy)-x^3-3x^2y(dx/dy)+6xy^2+2y^3(dx/dy)=0$ Isolate all terms with dx/dy onto one side of the equal sign and distribute the dx/dy out of each term: $dx/dy(4x^3y^2-3x^2y+2y^3)=2x^4y-x^3+6xy^2$ Isolate dx/dy by dividing both sides by the terms: $dx/dy=\frac{2x^4y-x^3+6xy^2}{4x^3y^2-3x^2y+2y^3}$
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