derivative of ln(1-(10/x))

Lösung

\frac{d}{d x} (ln (1 - \frac{10}{x}))

\frac{10}{x ( x - 10 )}

Schritte zur Lösung

\frac{d}{d x} (ln (1 - \frac{10}{x}))

Wende die Kettenregel an:

\frac{1}{1 - \frac{10}{x}} \frac{d}{d x} (1 - \frac{10}{x})

= \frac{1}{1 - \frac{10}{x}} \frac{d}{d x} (1 - \frac{10}{x})

\frac{d}{d x} (1 - \frac{10}{x}) = \frac{10}{x ^{2}}

= \frac{1}{1 - \frac{10}{x}} \cdot \frac{10}{x ^{2}}

Vereinfache

\frac{1}{1 - \frac{10}{x}} \cdot \frac{10}{x ^{2}} : \frac{10}{x ( x - 10 )}

= \frac{10}{x ( x - 10 )}

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