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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (3 x^{2} + 2 x) = 6 x + 2

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

= \frac{( 6 x + 2 ) ( 4 x - 2 ) - 4 ( 3 x ^{2} + 2 x )}{( 4 x - 2 ) ^{2}}

Vereinfache

\frac{( 6 x + 2 ) ( 4 x - 2 ) - 4 ( 3 x ^{2} + 2 x )}{( 4 x - 2 ) ^{2}} : \frac{3 x ^{2} - 3 x - 1}{( 2 x - 1 ) ^{2}}

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