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Beliebt Rechnen >

derivative of ln(1-2/x)

Lösung

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

Lösung

\frac{2}{x ( x - 2 )}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= \frac{2}{x ( x - 2 )}

Graph

Beliebte Beispiele

integral of (2/(sqrt(x))-3xsqrt(x)+2)

\int (\frac{2}{x} - 3 x x + 2) d x

integral from-1 to 2 of 4x(1-x^2)

\int_{- 1}^{2} 4 x (1 - x^{2}) d x

derivative of 21^x

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

integral of 5e^3

\int 5 e^{3} d x

derivative 1/((x^2-2x-5)^4)

d er i v a t i v e \frac{1}{( x ^{2} - 2 x - 5 ) ^{4}}