derivative (7+2x)/(9-8x)

Lösung

ableitung von

\frac{7 + 2 x}{9 - 8 x}

\frac{74}{( 9 - 8 x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{7 + 2 x}{9 - 8 x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 7 + 2 x ) ( 9 - 8 x ) - \frac{d}{d x} ( 9 - 8 x ) ( 7 + 2 x )}{( 9 - 8 x ) ^{2}}

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

\frac{d}{d x} (9 - 8 x) = - 8

= \frac{2 ( 9 - 8 x ) - ( - 8 ) ( 7 + 2 x )}{( 9 - 8 x ) ^{2}}

Vereinfache

\frac{2 ( 9 - 8 x ) - ( - 8 ) ( 7 + 2 x )}{( 9 - 8 x ) ^{2}} : \frac{74}{( 9 - 8 x ) ^{2}}

= \frac{74}{( 9 - 8 x ) ^{2}}

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