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Beliebt Rechnen >

derivative (3x+7)/(4x-5)

Lösung

ableitung von

\frac{3 x + 7}{4 x - 5}

Lösung

- \frac{43}{( 4 x - 5 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x + 7}{4 x - 5})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 3 x + 7 ) ( 4 x - 5 ) - \frac{d}{d x} ( 4 x - 5 ) ( 3 x + 7 )}{( 4 x - 5 ) ^{2}}

\frac{d}{d x} (3 x + 7) = 3

\frac{d}{d x} (4 x - 5) = 4

= \frac{3 ( 4 x - 5 ) - 4 ( 3 x + 7 )}{( 4 x - 5 ) ^{2}}

Vereinfache

\frac{3 ( 4 x - 5 ) - 4 ( 3 x + 7 )}{( 4 x - 5 ) ^{2}} : - \frac{43}{( 4 x - 5 ) ^{2}}

= - \frac{43}{( 4 x - 5 ) ^{2}}

Graph

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