derivative of (2x+5/(3x-1))

Lösung

\frac{d}{d x} (\frac{2 x + 5}{3 x - 1})

- \frac{17}{( 3 x - 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x + 5}{3 x - 1})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 2 x + 5 ) ( 3 x - 1 ) - \frac{d}{d x} ( 3 x - 1 ) ( 2 x + 5 )}{( 3 x - 1 ) ^{2}}

\frac{d}{d x} (2 x + 5) = 2

\frac{d}{d x} (3 x - 1) = 3

= \frac{2 ( 3 x - 1 ) - 3 ( 2 x + 5 )}{( 3 x - 1 ) ^{2}}

Vereinfache

\frac{2 ( 3 x - 1 ) - 3 ( 2 x + 5 )}{( 3 x - 1 ) ^{2}} : - \frac{17}{( 3 x - 1 ) ^{2}}

= - \frac{17}{( 3 x - 1 ) ^{2}}

\int (6 x^{5} - 4 x^{3} + \frac{1}{x}) d x

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