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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Multipliziere aus

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

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

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