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Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{6 ( x + 1 ) ^{2}}{( x - 1 ) ^{4}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

3 (\frac{x + 1}{x - 1})^{2} (- \frac{2}{( x - 1 ) ^{2}}) : - \frac{6 ( x + 1 ) ^{2}}{( x - 1 ) ^{4}}

= - \frac{6 ( x + 1 ) ^{2}}{( x - 1 ) ^{4}}

Graph

Beliebte Beispiele

integral of ysqrt(4+4y-4y^2)

\int y 4 + 4 y - 4 y^{2} d y

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derivative [x^2(x^2+6x)]^6

d er i v a t i v e [x^{2} (x^{2} + 6 x)]^{6}

integral of ((x^2-x+12))/(x^3+3x)

\int \frac{( x ^{2} - x + 12 )}{x ^{3} + 3 x} d x

derivative 4v^2-2

d er i v a t i v e 4 v^{2} - 2