Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - 7.1 Derivative of f(x)=bx and the Number e - Preliminary Questions - Page 326: 4

Answer

The derivative is negative whenever $\ln b $ is negative.

Work Step by Step

Suppose that $ y=b^x $, then we get $\ln y=x \ln b $. Then, $ y'=b^x\ln b $. Hence the derivative is negative whenever $\ln b $ is negative.
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