what is the derivative of ln(x)/x?

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You simply use the quotient rule. The derivative on ln(x) is simply the derivative of what you are taking the natural log of (in this case x), divided by that value. Hence the derivative of ln(x) = 1/x.  We then just use the quotient rule which is f(x) = g(x)/h(x) Therefore f ' (x) = (g'(x).h(x) - g(x).h'(x))/(h(x)^2)Rather messy to type, but hopefully you get the idea :P  Anyway for your function the derivative would be: ((1/x)(x) - ln(x)(1))/(x^2) which can be simplified to (1-ln(x)/(x^2). Hope this helps :D