derivative (x+7)/(x-7)

Lösung

ableitung von

\frac{x + 7}{x - 7}

- \frac{14}{( x - 7 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x + 7}{x - 7})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x + 7 ) ( x - 7 ) - \frac{d}{d x} ( x - 7 ) ( x + 7 )}{( x - 7 ) ^{2}}

\frac{d}{d x} (x + 7) = 1

\frac{d}{d x} (x - 7) = 1

= \frac{1 \cdot ( x - 7 ) - 1 \cdot ( x + 7 )}{( x - 7 ) ^{2}}

Vereinfache

\frac{1 \cdot ( x - 7 ) - 1 \cdot ( x + 7 )}{( x - 7 ) ^{2}} : - \frac{14}{( x - 7 ) ^{2}}

= - \frac{14}{( x - 7 ) ^{2}}

d er i v a t i v e \frac{( 2 x + 1 )}{x ^{3}}

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