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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

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