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?