# What is the derivative of #f(x)=log(x)/x# ?

The derivative is

This is an example of the the Quotient Rule:

Quotient Rule .

The quotient rule states that the derivative of a function

To put it more concisely:

For this specific example, we would let

Substituting these results into the quotient rule, we find:

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To find the derivative of ( f(x) = \frac{\log(x)}{x} ), you can use the quotient rule, which 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} ). Applying this rule to ( f(x) = \frac{\log(x)}{x} ), where ( g(x) = \log(x) ) and ( h(x) = x ), we get:

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

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