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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Vereinfache

\frac{- 1}{1 - x} : - \frac{1}{1 - x}

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

Graph

Beliebte Beispiele

derivative of x/(1+sqrt(1-x^2))

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

integral of (1100x)/(x^2+80)

\int \frac{1100 x}{x ^{2} + 80} d x

tangent f(x)=sqrt(x),(64,8)

t an g e n t f (x) = x, (64, 8)

(\partial)/(\partial x)(cos(x-y))

\frac{\partial}{\partial x} (cos (x - y))

derivative f(x)=sqrt(2x+4)

d er i v a t i v e f (x) = 2 x + 4