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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Vereinfache

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

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

Graph

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