derivative (2ln(x))/x

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Quotientenregel an:

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

= 2 \cdot \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

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

Vereinfache

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

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

\frac{d y}{d x} = 2 y (9 - y)

\frac{d x}{d t} = x (1 - \frac{1}{2500} x)

\int (x + 4) 8 x + x^{2} d x

\frac{d}{d x} (r^{2} - 7 x^{2})

\frac{d}{d x} (2 sec^{2} (x) tan (x))