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

The derivative of f(x)=(ln(x))/x is (1-ln(x))/(x^2)

What is the first derivative of f(x)=(ln(x))/x ?

The first derivative of f(x)=(ln(x))/x is (1-ln(x))/(x^2)

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derivative

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d x}{d 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}}

What is the derivative of f(x)=(ln(x))/x ?
The derivative of f(x)=(ln(x))/x is (1-ln(x))/(x^2)
What is the first derivative of f(x)=(ln(x))/x ?
The first derivative of f(x)=(ln(x))/x is (1-ln(x))/(x^2)