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Beliebt Rechnen >

derivative f(x)=(3x+4)/(3x-4)

Lösung

ableitung von

f (x) = \frac{3 x + 4}{3 x - 4}

Lösung

- \frac{24}{( 3 x - 4 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x + 4}{3 x - 4})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 3 x + 4 ) ( 3 x - 4 ) - \frac{d}{d x} ( 3 x - 4 ) ( 3 x + 4 )}{( 3 x - 4 ) ^{2}}

\frac{d}{d x} (3 x + 4) = 3

\frac{d}{d x} (3 x - 4) = 3

= \frac{3 ( 3 x - 4 ) - 3 ( 3 x + 4 )}{( 3 x - 4 ) ^{2}}

Vereinfache

\frac{3 ( 3 x - 4 ) - 3 ( 3 x + 4 )}{( 3 x - 4 ) ^{2}} : - \frac{24}{( 3 x - 4 ) ^{2}}

= - \frac{24}{( 3 x - 4 ) ^{2}}

Graph

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