Calculus 10th Edition

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

Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.1 Exercises: 53

Answer

$\displaystyle \frac{1-2\ln t}{t^{3}}$

Work Step by Step

Quotient rule, with $\displaystyle \frac{d}{dt}\ln t=\frac{1}{t}$ $g^{\prime}(t)=\displaystyle \frac{(\frac{1}{t})\cdot t^{2}-\ln t\cdot(2t)}{(t^{2})^{2}}=\frac{t-2t\ln t}{t^{4}}=\frac{t(1-2\ln t)}{t^{4}}=\frac{(1-2\ln t)}{t^{3}}$
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