Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - Review - Exercises - Page 197: 39


$\dfrac {3\cos \left( \tan \sqrt {1+x^{3}}\right) \times x^{2}}{2\sqrt {1+x^{3}}\times \cos \sqrt {1+x^{3}}} $

Work Step by Step

$\dfrac {d}{dx}\sin \left( \tan \sqrt {1+x^{3}}\right) =\cos \left( \tan \sqrt {1+x^{3}}\right) \times \left( \dfrac {d}{dx}\tan \sqrt {1+x^{3}}\right) =\dfrac {\cos \left( \tan \sqrt {1+x^{3}}\right) }{\cos^ 2\sqrt {1+x^{3}}}\times \left( \dfrac {d}{dx}\sqrt {1+x^{3}}\right) =\dfrac {\cos \left( \tan \sqrt {1+x^{3}}\right) }{\cos \sqrt {1+x^{3}}}\times \dfrac {1}{2\sqrt {1+x^{3}}}\times \dfrac {d}{dx}\left( 1+x^{3}\right) =\dfrac {3\cos \left( \tan \sqrt {1+x^{3}}\right) \times x^{2}}{2\sqrt {1+x^{3}}\times \cos \sqrt {1+x^{3}}} $
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