Differential Equations and Linear Algebra (4th Edition)

Published by Pearson
ISBN 10: 0-32196-467-5
ISBN 13: 978-0-32196-467-0

Chapter 1 - First-Order Differential Equations - 1.3 The Geometry of First-Order Differential Equations - Problems - Page 32: 8



Work Step by Step

Differentiate the equation in respect to $x$, remembering to use chain rule. $$2c\frac{dy}{dx}=2x$$ Solve for the slope of the tangent line $\frac{dy}{dx}$ to get a slope of $$\frac{dy}{dx}=\frac{x}{c}$$
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