## Calculus (3rd Edition)

Published by W. H. Freeman

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

#### Answer

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

#### 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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