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Beliebt Rechnen >

derivative ln(5x+ln(3x))

Lösung

ableitung von

ln (5 x + ln (3 x))

Lösung

\frac{5 x + 1}{x ( 5 x + ln ( 3 x ) )}

Schritte zur Lösung

\frac{d}{d x} (ln (5 x + ln (3 x)))

Wende die Kettenregel an:

\frac{1}{5 x + ln ( 3 x )} \frac{d}{d x} (5 x + ln (3 x))

= \frac{1}{5 x + ln ( 3 x )} \frac{d}{d x} (5 x + ln (3 x))

\frac{d}{d x} (5 x + ln (3 x)) = 5 + \frac{1}{x}

= \frac{1}{5 x + ln ( 3 x )} (5 + \frac{1}{x})

Vereinfache

\frac{1}{5 x + ln ( 3 x )} (5 + \frac{1}{x}) : \frac{5 x + 1}{x ( 5 x + ln ( 3 x ) )}

= \frac{5 x + 1}{x ( 5 x + ln ( 3 x ) )}

Graph

Beliebte Beispiele

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