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Beliebt Rechnen >

derivative (11)/(ln(x))

Lösung

ableitung von

\frac{11}{ln ( x )}

Lösung

- \frac{11}{x ln ^{2} ( x )}

Schritte zur Lösung

\frac{d}{d x} (\frac{11}{ln ( x )})

Entferne die Konstante:

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

= 11 \frac{d}{d x} (\frac{1}{ln ( x )})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= 11 \frac{d}{d x} (ln^{- 1} (x))

Wende die Kettenregel an:

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

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

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

= 11 (- \frac{1}{( ln ( x ) ) ^{2}} \cdot \frac{1}{x})

Vereinfache

11 (- \frac{1}{ln ^{2} ( x )} \cdot \frac{1}{x}) : - \frac{11}{x ln ^{2} ( x )}

= - \frac{11}{x ln ^{2} ( x )}

Graph

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