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.
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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
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