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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

2 \cdot \frac{1 + x}{1 - x} \cdot \frac{2}{( 1 - x ) ^{2}} : \frac{4 ( 1 + x )}{( 1 - x ) ^{3}}

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

Graph

Beliebte Beispiele

(d^4)/(dx^4)(1/(3x+1))

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

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\int 2 x^{3} + 4 x + 5 d x

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x \to π lim (sin (\frac{11}{6}))

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