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This is a lognormal distribution with $\displaystyle \sigma=1$ Log-normal distribution - Wikipedia, the free encyclopedia I guess you need to just differentiate r(x) via the quotient rule to decide which is correct.
hi.. i tried this differentiating this as you had said, but was unable to get a meaningful result. The expression just got complicated and complicated. (Infact I doubt I even differentiated it properly)
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