Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.3 Derivatives Of Inverse Functions; Derivatives And Integrals Involving Exponential Functions - Exercises Set 6.3: 45

Answer

True.

Work Step by Step

Logarithm rules state that a logarithm with base $b$ can be rewritten as $$\frac{ln(x)}{ln(b)}$$ Taking the derivative of the new expression, $\frac{ln|x|}{ln(b)}$, by separating the constant $\frac{1}{ln(b)}$ yields $$\frac{1}{x \times ln(b)}=\frac{1}{xln(b)}$$
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