Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.1 Parametric Equations - Exercises - Page 604: 54


$$ \frac{d y}{d x}= \frac{2t}{e^t} $$ and at $t=1$, we have $$ \frac{d y}{d x}= \frac{2}{e}. $$

Work Step by Step

Since $x=e^t$ and $y=t^2$, then we have $$ \frac{d y}{d x}= \frac{y^{\prime}}{x^{\prime}}=\frac{2t}{e^t} $$ and at $t=1$, we have $$ \frac{d y}{d x}= \frac{2}{e}. $$
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