Calculus: Early Transcendentals (2nd Edition)

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

Chapter 3 - Derivatives - 3.5 Derivatives of Trigonometric Functions - 3.5 Exercises: 20

Answer

\[\frac{{dy}}{{dx}} = \cos x + 2{e^{0.5x}}\]

Work Step by Step

\[\begin{gathered} y = \sin x + 4{e^{0.5x}} \hfill \\ \hfill \\ differentiate \hfill \\ \hfill \\ \frac{{dy}}{{dx}} = \,\,{\left[ {\sin x} \right]^,} + \,\,{\left[ {4{e^{0.5x}}} \right]^,} \hfill \\ \frac{{dy}}{{dx}} = \,\,{\left[ {\sin x} \right]^,} + \,\,4{\left[ {{e^{0.5x}}} \right]^,} \hfill \\ \hfill \\ therefore \hfill \\ \hfill \\ \frac{{dy}}{{dx}} = \cos x + 4\,\left( {0.5} \right){e^{0.5x}} \hfill \\ \hfill \\ multiply \hfill \\ \hfill \\ \frac{{dy}}{{dx}} = \cos x + 2{e^{0.5x}} \hfill \\ \hfill \\ \end{gathered} \]
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