Answer
$\frac{1}{x}$
Work Step by Step
Using the log rule of $\log(ab)=\log(a)+\log(b)$, $\ln(5x)$ can be written as $$\ln (5x)=\ln(x)+\ln(5)$$ Taking the derivative of this expression yields $$\frac{d}{dx}(\ln(5x))=\frac{1}{x}.$$
Calculus, 10th Edition (Anton)
by Anton, Howard
Published by
Wiley
ISBN 10:
0-47064-772-8
ISBN 13:
978-0-47064-772-1
Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.2 Derivatives And Integrals Involving Logarithmic Functions - Exercises Set 6.2 - Page 425: 1
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