Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.4 Exercises: 35

Answer

$y’=\frac{e^{\sqrt{x}}} {2\sqrt{x}}$

Work Step by Step

$y=e^{\sqrt{x}}$ let u=$\sqrt{x}$ u'=$\frac{1}{2}x^{-\frac{1}{2}}$ $\frac{d}{dx}e^u=u'e^u$ $y’=\frac{1}{2}x^{-\frac{1}{2}}e^{\sqrt{x}}$ $=\frac{e^{\sqrt{x}}} {2\sqrt{x}}$
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