What is (\partial}{\partial x}(\frac{ln(x))/x) ?

The answer to (\partial}{\partial x}(\frac{ln(x))/x) is (1-ln(x))/(x^2)

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(\partial}{\partial x}(\frac{ln(x))/x)

\frac{\partial}{\partial x} (\frac{ln ( x )}{x})

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

Solution steps

\frac{\partial}{\partial x} (\frac{ln ( x )}{x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{\partial}{\partial x} ( ln ( x ) ) x - \frac{\partial}{\partial x} ( x ) ln ( x )}{x ^{2}}

\frac{\partial}{\partial x} (ln (x)) = \frac{1}{x}

\frac{\partial}{\partial x} (x) = 1

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

Simplify

\frac{\frac{1}{x} x - 1 \cdot ln ( x )}{x ^{2}} : \frac{1 - ln ( x )}{x ^{2}}

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

\frac{d}{d x} (5 \cdot 2^{x})

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f (x) = \frac{2 x}{x ^{2} - 7}

What is (\partial}{\partial x}(\frac{ln(x))/x) ?
The answer to (\partial}{\partial x}(\frac{ln(x))/x) is (1-ln(x))/(x^2)