Answer
$(f(g(x))'=-2x\sin(x^{2}+1)$
$(g(f(x))'=-2\cos x\sin x$
Work Step by Step
$(f(g(x))'=f'(g(x))\times g'(x)$
$=-\sin(x^{2}+1)\times2x$
$=-2x\sin(x^{2}+1)$
$(g(f(x))'=g'(f(x))\times f'(x)$
$=2\cos x\times-\sin x=-2\cos x\sin x$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 3 - Differentiation - 3.7 The Chain Rule - Exercises - Page 146: 27
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