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

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

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

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

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

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

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

\int_{0}^{1} \frac{5}{1 + t ^{2}} d t

\int x^{5} (x^{6} + 5)^{5} d x

ln (x^{2} - 1)

f (x) = x^{2} e^{11 x}

\int \frac{x ^{3}}{x ^{4} + 1} d x

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