Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 3: Derivatives - Section 3.5 - Derivatives of Trigonometric Functions - Exercises 3.5: 17

Answer

The Derivative is: $y'=3x^2\sin x\cos x+x^3\cos^2 x-x^3\sin^2 x$

Work Step by Step

$y=x^3\sin x\cos x$ Applying Derivative Rules: $y'=f'(x)\cdot g(x)+f(x)\cdot g'(x)$ $y'=(3x^{3-1})(\sin x\cos x)+(x^3)((\cos x)(\cos x)+(\sin x)(-\sin x))$ $y'=3x^2\sin x\cos x+x^3\cos^2 x-x^3\sin^2 x$
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