The discussion centers on finding the first and second derivatives of the vector function r(t) = ln(t)i + j, where t > 0. The correct first derivative is confirmed as r'(t) = (1/t)i - (1/t^2)j, despite initial confusion regarding the constant nature of the j component. Participants suggest that the original function may contain a misprint and propose an alternative form, r(t) = ln(t)i + (1/t)j, for clarity. The consensus emphasizes proceeding with the problem as stated in the assignment.
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Char. Limit said:That doesn't make too much sense if r(t) is supposed to be constant along the j unit vector. My best guess is that it's probably a misprint, and that r(t) is supposed to be r(t)=ln(t) i + 1/t j. That said, if this is for an assignment, proceed with the problem as written, which you're on the right track so far.