Answer
$\frac{dy}{dx} = \ln(10)$
Work Step by Step
If $f(x) = b^x$, then $f'(x) = b^x\ln(b)$
$y = \ln(10^x) $
Chain Rule:
$\frac{dy}{dx} = (10^x)(\ln(10))(\frac{1}{10^x}) = \ln(10)$
Calculus: Early Transcendentals (2nd Edition)
by Briggs, Bill L.; Cochran, Lyle; Gillett, Bernard
Published by
Pearson
ISBN 10:
0321947347
ISBN 13:
978-0-32194-734-5
Chapter 3 - Derivatives - 3.9 Derivatives of Logarithmic and Exponential Functions - 3.9 Exercises - Page 211: 30
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