# How do I find the derivative of #lnx/x^2#?

Use the quotient rule:

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To find the derivative of ( \frac{\ln(x)}{x^2} ), you can use the quotient rule of differentiation, which states that if you have a function in the form ( \frac{f(x)}{g(x)} ), the derivative is given by:

[ \left( \frac{f'(x) \cdot g(x) - f(x) \cdot g'(x)}{(g(x))^2} \right) ]

Now, applying the quotient rule to ( \frac{\ln(x)}{x^2} ):

[ f(x) = \ln(x) ] [ g(x) = x^2 ]

[ f'(x) = \frac{1}{x} ] [ g'(x) = 2x ]

[ \frac{d}{dx} \left( \frac{\ln(x)}{x^2} \right) = \frac{\frac{1}{x} \cdot x^2 - \ln(x) \cdot 2x}{(x^2)^2} ] [ = \frac{x - 2x \ln(x)}{x^4} ]

So, the derivative of ( \frac{\ln(x)}{x^2} ) is ( \frac{x - 2x \ln(x)}{x^4} ).

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