# What is the derivative of #lnx / x#?

Using quotient rule, which states that for

Solving:

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The derivative of ( \frac{\ln(x)}{x} ) can be found using the quotient rule. The quotient rule states that if ( f(x) = \frac{g(x)}{h(x)} ), then ( f'(x) = \frac{g'(x)h(x) - g(x)h'(x)}{(h(x))^2} ).

Let ( g(x) = \ln(x) ) and ( h(x) = x ).

Then ( g'(x) = \frac{1}{x} ) and ( h'(x) = 1 ).

Using the quotient rule, we have:

[ f'(x) = \frac{\frac{1}{x} \cdot x - \ln(x) \cdot 1}{(x)^2} ]

[ = \frac{1 - \ln(x)}{x^2} ]

So, the derivative of ( \frac{\ln(x)}{x} ) is ( \frac{1 - \ln(x)}{x^2} ).

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