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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{1}{1 - x}

Schritte zur Lösung

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

Vereinfache

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

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

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

= \frac{1}{1 - x}

Graph

Beliebte Beispiele

fläche y=4x^2,y=x^2+6

a re a y = 4 x^{2}, y = x^{2} + 6

limit as x approaches 7 of x+2

x \to 7 lim (x + 2)

integral of xe^xln(x-1)

\int x e^{x} ln (x - 1) d x

integral of (sin^5(ln(x)))/x

\int \frac{sin ^{5} ( ln ( x ) )}{x} d x

limit as x approaches 0 of (sqrt(5+x)-sqrt(5))/(2x)

x \to 0 lim (\frac{5 + x - 5}{2 x})