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: 50

Answer

\[\frac{{dy}}{{dx}} = - 84{x^2}{\cos ^3}\,\left( {7{x^3}} \right)\,\left( {\sin 7{x^3}} \right)\]

Work Step by Step

\[\begin{gathered} {\cos ^4}\,\left( {7{x^3}} \right) \hfill \\ \hfill \\ Chain\,\,rule \hfill \\ \hfill \\ \frac{{dy}}{{dx}} = {f^,}\,\left( {g\,\left( t \right)} \right) \cdot {g^,}\,\left( t \right) \hfill \\ \hfill \\ \frac{{dy}}{{dx}} = 4{\cos ^3}\,\left( {7{x^3}} \right)\,\left( { - \sin 7{x^3}} \right)\,{\left( {7{x^3}} \right)^,} \hfill \\ \hfill \\ therefore \hfill \\ \hfill \\ \frac{{dy}}{{dx}} = - 4{\cos ^3}\,\left( {7{x^3}} \right)\,\left( {\sin 7{x^3}} \right)\,\left( {21{x^2}} \right) \hfill \\ \hfill \\ simplify \hfill \\ \hfill \\ \frac{{dy}}{{dx}} = - 84{x^2}{\cos ^3}\,\left( {7{x^3}} \right)\,\left( {\sin 7{x^3}} \right) \hfill \\ \end{gathered} \]
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