Calculus (3rd Edition)

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

Chapter 3 - Differentiation - 3.3 Product and Quotient Rules - Exercises - Page 122: 34


$$ g'(z)=-z^{-2}(z-2)(z^2+1)+z^{-1}(z^2+1)+2(z-2)$$

Work Step by Step

Recall the product rule: $(uv)'=u'v+uv'$ For the sake of simplicity, we rewrite $ g(z)$ as follows $$ g(z)=z^{-1}(z-2)(z^2+1)$$ Using the product rule, the derivative $ g'(z)$ is given by $$ g'(z)=-z^{-2}(z-2)(z^2+1)+z^{-1}(z^2+1)+2zz^{-1}(z-2)\\ =-z^{-2}(z-2)(z^2+1)+z^{-1}(z^2+1)+2(z-2)$$
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