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Beliebt Rechnen >

derivative of log_{3}(8x-1)

Lösung

\frac{d}{d x} (lo g_{3} (8 x - 1))

Lösung

\frac{8}{ln ( 3 ) ( 8 x - 1 )}

Schritte zur Lösung

\frac{d}{d x} (lo g_{3} (8 x - 1))

Wende die log Regel an:

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

= \frac{d}{d x} (\frac{ln ( 8 x - 1 )}{ln ( 3 )})

Entferne die Konstante:

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

= \frac{1}{ln ( 3 )} \frac{d}{d x} (ln (8 x - 1))

Wende die Kettenregel an:

\frac{1}{8 x - 1} \frac{d}{d x} (8 x - 1)

= \frac{1}{8 x - 1} \frac{d}{d x} (8 x - 1)

\frac{d}{d x} (8 x - 1) = 8

= \frac{1}{ln ( 3 )} \cdot \frac{1}{8 x - 1} \cdot 8

Vereinfache

\frac{1}{ln ( 3 )} \cdot \frac{1}{8 x - 1} \cdot 8 : \frac{8}{ln ( 3 ) ( 8 x - 1 )}

= \frac{8}{ln ( 3 ) ( 8 x - 1 )}

Graph

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