Answer
$y’=\frac{y(1-6x^2)}{(1+y)}$
Work Step by Step
$4x^3+lny^2+2y=2x$
$12x^2+\frac{2y}{y^2}y’+2y’=2$
$\frac{2}{y}y’+2y’=2-12x^2$
Next, we multiply everything by $y$:
$2y’+2yy’=2y-12x^2y$
$y’(2+2y)=2y(1-6x^2)$
$y’=\frac{y(1-6x^2)}{(1+y)}$
Calculus 10th Edition
by Larson, Ron; Edwards, Bruce H.
Published by
Brooks Cole
ISBN 10:
1-28505-709-0
ISBN 13:
978-1-28505-709-5
Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.1 Exercises - Page 326: 75
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