Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - 7.3 Logarithms and Their Derivatives - Exercises - Page 343: 34


$$ y' =\frac{1}{t}+\ln 5.$$

Work Step by Step

Recall the product rule: $(uv)'=u'v+uv'$ Recall that $(\ln x)'=\dfrac{1}{x}$ Recall that $(e^x)'=e^x$ Since $ y=\ln(t5^t)$, then we have $$ y'=\frac{ 5^t+t 5^t \ln 5}{t5^t}=\frac{1+t \ln 5}{t }=\frac{1}{t}+\ln 5.$$
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