Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.3 Differentiation Formulas - 2.3 Exercises: 27

Answer

$F'(y)=5+\frac{14}{y^2}+\frac{9}{y^4}$

Work Step by Step

$F(y)=(\frac{1}{y^2}-\frac{3}{y^4})(y+5y^3)$ Rewrite into exponent form. $F(y)=(y^{-2}-3y^{-4})(y+5y^3)$ Use the product rule. $F'(y)=(y^{-2}-3y^{-4})(1+15y^2)+(y+5y^3)(-2y^{-3}+12y^{-5})$ Distribute. $F'(y)=y^{-2}+15-3y^{-4}-45y^{-2}-2y^{-2}+12y^{-4}-10+60y^{-2}$ Combine like terms. $F'(y)=5+14y^{-2}+9y^{-4}$ Rewrite. $F'(y)=5+\frac{14}{y^2}+\frac{9}{y^4}$
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