Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 6 - Applications of the Derivative - 6.4 Implicit Differentiation - 6.4 Exercises - Page 334: 4



Work Step by Step

$7x^{2}=5y^{2}+4xy + 1$ Find dy/dx by implicit differentiation $\frac{dx}{dy}(7x^{2}-5y^{2}-4xy)=\frac{dx}{dy}(1)$ $14x -10y\frac{dy}{dx} - 4x\frac{dy}{dx}−4y=0$ $(4x+10y)\frac{dy}{dx}=14x-4y$ $\frac{dy}{dx}=\frac{14x-4y}{4x+10y}=\frac{7x-2y}{2x+5y}$
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