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

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

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

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

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derivative of

f (x) = \frac{ln ( x )}{x}

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

\frac{d x}{d x} = 1

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

Simplify

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

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

x \to 0 lim ((e^{2 x} - 5 x)^{2})

\int \frac{9}{x ( x ^{4} + 8 )} d x

y = \frac{5 x}{x + 4}, (1, 1)

\int \frac{cos ( x )}{sin ( 2 x )} d x

\frac{1}{x ^{2}}, 2

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