derivative (1-4x)/(2+x)

Lösung

ableitung von

\frac{1 - 4 x}{2 + x}

- \frac{9}{( 2 + x ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (1 - 4 x) = - 4

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

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

Vereinfache

\frac{( - 4 ) ( 2 + x ) - 1 \cdot ( 1 - 4 x )}{( 2 + x ) ^{2}} : - \frac{9}{( 2 + x ) ^{2}}

= - \frac{9}{( 2 + x ) ^{2}}

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