Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 2 - The Derivative - 2.5 Derivatives of Trigonometric Functions - Exercises Set 2.5: 4

Answer

$=4sinxcosx$

Work Step by Step

Take out the $2$ from the derivative, it can be multiplied to the answer at the end. Splitting $sin^{2}(x)$ into $sinx\times\sin(x)$ allows one to do the product rule, stating $f=sinx$ and $g=sinx$. Using $(fg)'=f'g+g'f$, the answer becomes $2(sinxcosx+sinxcosx)=2(2sinxcosx)=4sinxcosx.$
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