Answer
$2 \cosh {\dfrac{x}{3}}$
Work Step by Step
Given: $y=6 \sinh {\dfrac{x}{3}}$
Since, we know that $\dfrac{d}{dx} (\sinh x)=\cosh x$
This implies
$\dfrac{dy}{dx}=6 \cosh {\dfrac{x}{3}} (\dfrac{1}{3})$
or, $=2 \cosh {\dfrac{x}{3}}$
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0-32187-896-5
ISBN 13:
978-0-32187-896-0
Chapter 7: Transcendental Functions - Section 7.7 - Hyperbolic Functions - Exercises 7.7 - Page 430: 13
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