University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Section 3.6 - The Chain Rule - Exercises - Page 158: 58



Work Step by Step

$$\frac{dy}{dt}=\frac{d}{dt}\Big(e^{\sin(t/2)}\Big)^3$$ According to the Chain Rule: $$\frac{dy}{dt}=3\Big(e^{\sin(t/2)}\Big)^2\frac{d}{dt}\Big(e^{\sin(t/2)}\Big)'$$ $$\frac{dy}{dt}=3e^{2\sin(t/2)}e^{\sin(t/2)}\frac{d}{dt}(\sin(t/2))$$ $$\frac{dy}{dt}=3e^{3\sin(t/2)}\cos(t/2)\frac{d}{dt}(t/2)$$ $$\frac{dy}{dt}=\frac{3}{2}e^{3\sin(t/2)}\cos(t/2)$$
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