derivative of (sqrt(2x)/(ln(x)))

Lösung

\frac{d}{d x} (\frac{2 x}{ln ( x )})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x}{ln ( x )})

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (\frac{x ^{3}}{1 - x ^{3}})

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