Calculus 10th Edition

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

Chapter 2 - Differentiation - Review Exercises: 36

Answer

$y'=\dfrac{x\cos{x}-4\sin{x}}{x^5}.$

Work Step by Step

Using the quotient rule: $y'=(\frac{u(x)}{v(x)})'=\frac{u'(x)v(x)-v'(x)u(x)}{(v(x))^2}$ $u(x)=\sin{x}; u'(x)=\cos{x}$ $v(x)=x^4; v'(x)=4x^3$ $y'=\dfrac{(\cos{x})(x^4)-(4x^3)(\sin{x})}{(x^4)^2}$ $=\dfrac{x^3(x\cos{x}-4\sin{x})}{x^8}$ $=\dfrac{x\cos{x}-4\sin{x}}{x^5}.$
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