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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{2}{( x - 1 ) ^{3}}

Schritte zur Lösung

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

Vereinfache

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

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

- \frac{2}{( x - 1 ) ^{3}} \frac{d}{d x} (x - 1)

= - \frac{2}{( x - 1 ) ^{3}} \frac{d}{d x} (x - 1)

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

= - (- \frac{2}{( x - 1 ) ^{3}} \cdot 1)

Vereinfache

= \frac{2}{( x - 1 ) ^{3}}

Graph

Beliebte Beispiele

y^'=(2y^2)+xy^2

y^{^{'}} = (2 y^{2}) + x y^{2}

f^'(x)=2x-3/(x^4)

f^{^{'}} (x) = 2 x - \frac{3}{x ^{4}}

tangent f(x)= 2/(3x+1)

t an g e n t f (x) = \frac{2}{3 x + 1}

integral from 0 to 1 of 7e^{-7sqrt(x)}

\int_{0}^{1} 7 e^{- 7 x} d x

limit as x approaches 5 of (x+2)/(x-4)

x \to 5 lim (\frac{x + 2}{x - 4})