Calculus (3rd Edition)

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

Chapter 3 - Differentiation - Chapter Review Exercises - Page 164: 55


$$ R'(2)= -\frac{57}{16}.$$

Work Step by Step

Given $ R(x)=f(x)/g(x)$, then we have $ R'(x)=\frac{g(x)f'(x)-f(x)g'(x)}{g^2(x)}$ and hence $$ R'(2)=\frac{g(2)f'(2)-f(2)g'(2)}{g^2(2)}=\frac{4(-3)-5(9)}{4^2}\\ =\frac{-12-45}{16}=-\frac{57}{16}.$$
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