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Beliebt Rechnen >

derivative of ((x+3/(x-1))^2)

Lösung

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

Lösung

- \frac{8 ( x + 3 )}{( x - 1 ) ^{3}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{x + 3}{x - 1}) = - \frac{4}{( x - 1 ) ^{2}}

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

Vereinfache

2 \cdot \frac{x + 3}{x - 1} (- \frac{4}{( x - 1 ) ^{2}}) : - \frac{8 ( x + 3 )}{( x - 1 ) ^{3}}

= - \frac{8 ( x + 3 )}{( x - 1 ) ^{3}}

Graph

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