Calculus (3rd Edition)

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

Chapter 3 - Differentiation - 3.6 Trigonometric Functions - Exercises: 5

Answer

$cos^{2}(x)-sin^{2}(x)$

Work Step by Step

Using the product rule for differentiation, or $[uv]'=u'v+vu'$, the derivative of $sin(x)cos(x)$ is $sin(x)[cos(x)]'+[sin(x)]'cos(x)$, or $cos^{2}(x)-sin^{2}(x)$.
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