Calculus (3rd Edition)

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


$(f(g(x))'=-2x\sin(x^{2}+1)$ $(g(f(x))'=-2\cos x\sin x$

Work Step by Step

$(f(g(x))'=f'(g(x))\times g'(x)$ $=-\sin(x^{2}+1)\times2x$ $=-2x\sin(x^{2}+1)$ $(g(f(x))'=g'(f(x))\times f'(x)$ $=2\cos x\times-\sin x=-2\cos x\sin x$
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