Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.3 Exercises - Page 125: 11


The derivative is $\frac{x\cos(x)-2\sin(x)}{x^3}$.

Work Step by Step

Using the quotient rule: $g'(x)=(\frac{u(x)}{v(x)})'=\frac{u'(x)v(x)-v'(x)u(x)}{(v(x))^2}$ $u(x)=sin(x); u'(x)=cos(x)$ $v(x)=x^2; v'(x)=2x$ $g'(x)=\frac{(cos(x)(x^2)-(sin(x))(2x)}{(x^2)^2}=$ $\frac{x(xcos(x)-2sin(x))}{x^4}=\frac{x\cos(x)-2\sin(x)}{x^3}$
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