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Beliebt Rechnen >

derivative of log_{x}(3)

Lösung

\frac{d}{d x} (lo g_{x} (3))

Lösung

- \frac{ln ( 3 )}{x ln ^{2} ( x )}

Schritte zur Lösung

\frac{d}{d x} (lo g_{x} (3))

Wende die log Regel an:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} (\frac{ln ( 3 )}{ln ( x )})

Entferne die Konstante:

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

= ln (3) \frac{d}{d x} (\frac{1}{ln ( x )})

Wende die Quotientenregel an:

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

= ln (3) \frac{\frac{d}{d x} ( 1 ) ln ( x ) - \frac{d}{d x} ( ln ( x ) ) 1}{( ln ( x ) ) ^{2}}

\frac{d}{d x} (1) = 0

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

= ln (3) \frac{0 \cdot ln ( x ) - \frac{1}{x} \cdot 1}{( ln ( x ) ) ^{2}}

Vereinfache

ln (3) \frac{0 \cdot ln ( x ) - \frac{1}{x} \cdot 1}{ln ^{2} ( x )} : - \frac{ln ( 3 )}{x ln ^{2} ( x )}

= - \frac{ln ( 3 )}{x ln ^{2} ( x )}

Graph

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