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Beliebt Rechnen >

derivative f(x)=(1-2x)/(5+x)

Lösung

ableitung von

f (x) = \frac{1 - 2 x}{5 + x}

Lösung

- \frac{11}{( 5 + x ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (5 + x) = 1

= \frac{( - 2 ) ( 5 + x ) - 1 \cdot ( 1 - 2 x )}{( 5 + x ) ^{2}}

Vereinfache

\frac{( - 2 ) ( 5 + x ) - 1 \cdot ( 1 - 2 x )}{( 5 + x ) ^{2}} : - \frac{11}{( 5 + x ) ^{2}}

= - \frac{11}{( 5 + x ) ^{2}}

Graph

Beliebte Beispiele

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