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I Question about d/dx [ln(x)]

  1. Sep 13, 2017 #1
    I feel like I might be missing something here, but how is the deriviative of ln(x) equal to 1/x? The graph of ln(x) only has valid x values to the right of the x axis. The graph for 1/x has valid values for x for all real numbers except for 0. Am I to deduce that functions and their derivatives do not always necessarily occupy the same domain? If so are the values to the left of the y axis of any significance or should they just be ignored?
  2. jcsd
  3. Sep 13, 2017 #2


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    Staff: Mentor

    For ##x < 0## we get with the chain rule ##\frac{d}{dx}\log (-x) = \frac{1}{-x}\cdot (-1) = \frac{1}{x}## and both give ##\frac{d}{dx}\log |x| = \frac{1}{x}## for ##x \neq 0## which is the proper formula for the derivative of the logarithm function for both branches of ##\frac{1}{x}##.
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