Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 3 - Derivatives - 3.7 The Chain Rule - 3.7 Exercises - Page 192: 59


$y= xe^{x^2+1}[2sin(x^3)+3xcos(x^3)]$

Work Step by Step

Chain Rule $\frac{d}{dx}[f(g(x))] = f'(g(x)) \times g'(x)$ $y=e^{x^2+1}sin(x^3)$ Product Rule: $y=(\frac{d}{dx}e^{x^2+1})(sin(x^3)) + (e^{x^2+1})(\frac{d}{dx}sin(x^3))$ Chain Rule: $y=(2xe^{x^2+1})sin(x^3) + e^{x^2+1}(3x^2cos(x^3)) = xe^{x^2+1}[2sin(x^3)+3xcos(x^3)]$
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