Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 15 - Differentiation in Several Variables - 15.3 Partial Derivatives - Exercises - Page 781: 36


$$ z_x= \sin( x) \sinh(t-\cos x) ,\quad z_t= \sinh(t-\cos x) . $$

Work Step by Step

Recall that $(\cosh x)'=\sinh x$ Recall that $(\cos x)'=-\sin x$. Since $ z=\cosh (t-\cos x)$, by using the chain rule, we have $$ z_x= \sinh(t-\cos x) (\sin x)=\sin( x) \sinh(t-\cos x) ,\\ z_t= \sinh(t-\cos x) (1)= \sinh(t-\cos x) . $$
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