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Beliebt Rechnen >

derivative of (sqrt(x)/(ln(x)))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of (\sqrt[3]{x^4})

\int (3 x^{4}) d x

4t((dy)/(dt))-y=sqrt(t)

4 t (\frac{d y}{d t}) - y = t

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\int \frac{1}{144 + x ^{2}} d x

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integral from 0 to 1 of 1/(x^{0.5)}

\int_{0}^{1} \frac{1}{x ^{0.5}} d x