Answer
False
Work Step by Step
$$\eqalign{
& {\text{Let }}f\left( x \right) = \ln \left| x \right|{\text{ and }}g\left( x \right) = \ln x \cr
& {\text{The derivative of }}g\left( x \right) = \ln x{\text{ is}} \cr
& g'\left( x \right) = \frac{1}{x},{\text{ }} \cr
& {\text{The domain of }}\ln x{\text{ is }}D:\left( {0,\infty } \right) \cr
& g'\left( x \right) = \frac{1}{x}{\text{ is always positive for all }}\left( {0,\infty } \right),{\text{ then the slope}} \cr
& {\text{is positive for }}\left( {0,\infty } \right). \cr
& \cr
& {\text{The domain of }}f\left( x \right) = \ln \left| x \right|{\text{ is }}D:\left( { - \infty ,0} \right) \cup \left( {0,\infty } \right) \cr
& f'\left( x \right) = \frac{1}{x},{\text{ the slope is defined for }}x < 0{\text{ then the derivatives}} \cr
& {\text{are not equal}}.{\text{ But for }}x > {\text{0 the statement is True}} \cr} $$
