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Beliebt Rechnen >

derivative of 4/((1-x^3))

Lösung

\frac{d}{d x} (\frac{4}{( 1 - x ) ^{3}})

Lösung

\frac{12}{( 1 - x ) ^{4}}

Schritte zur Lösung

\frac{d}{d x} (\frac{4}{( 1 - x ) ^{3}})

Entferne die Konstante:

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

= 4 \frac{d}{d x} (\frac{1}{( 1 - x ) ^{3}})

Wende Exponentenregel an:

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

= 4 \frac{d}{d x} ((1 - x)^{- 3})

Wende die Kettenregel an:

- \frac{3}{( 1 - x ) ^{4}} \frac{d}{d x} (1 - x)

= - \frac{3}{( 1 - x ) ^{4}} \frac{d}{d x} (1 - x)

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

= 4 (- \frac{3}{( 1 - x ) ^{4}} (- 1))

Vereinfache

4 (- \frac{3}{( 1 - x ) ^{4}} (- 1)) : \frac{12}{( 1 - x ) ^{4}}

= \frac{12}{( 1 - x ) ^{4}}

Graph

Beliebte Beispiele

integral of (e^x)^3

\int (e^{x})^{3} d x

limit as x approaches pi of cos(x-pi)

x \to π lim (cos (x - π))

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\int 0.2 + 25 x - 200 x^{2} + 675 x^{3} - 900 x^{4} + 400 x^{5} d x

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\int \frac{1}{x ( 2 x + 5 ) ^{2}} d x

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\frac{d}{d x} (2 5^{x})