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Beliebt Rechnen >

derivative of ln(1/(6+x))

Lösung

\frac{d}{d x} (ln (\frac{1}{6 + x}))

Lösung

- \frac{1}{6 + x}

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{1}{6 + x}))

Vereinfache

ln (\frac{1}{6 + x}) : - ln (6 + x)

= \frac{d}{d x} (- ln (6 + x))

Entferne die Konstante:

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

= - \frac{d}{d x} (ln (6 + x))

Wende die Kettenregel an:

\frac{1}{6 + x} \frac{d}{d x} (6 + x)

= \frac{1}{6 + x} \frac{d}{d x} (6 + x)

\frac{d}{d x} (6 + x) = 1

= - \frac{1}{6 + x} \cdot 1

Vereinfache

= - \frac{1}{6 + x}

Graph

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