derivative of (2x+1/(3x-4))

Lösung

\frac{d}{d x} (\frac{2 x + 1}{3 x - 4})

- \frac{11}{( 3 x - 4 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x + 1}{3 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 + 1 ) ( 3 x - 4 ) - \frac{d}{d x} ( 3 x - 4 ) ( 2 x + 1 )}{( 3 x - 4 ) ^{2}}

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

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

= \frac{2 ( 3 x - 4 ) - 3 ( 2 x + 1 )}{( 3 x - 4 ) ^{2}}

Vereinfache

\frac{2 ( 3 x - 4 ) - 3 ( 2 x + 1 )}{( 3 x - 4 ) ^{2}} : - \frac{11}{( 3 x - 4 ) ^{2}}

= - \frac{11}{( 3 x - 4 ) ^{2}}

\frac{d}{d x} (2 - 10 x)

\int cos (m x) d x

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