derivative f(x)=(2x-1)/(2x+1)

Lösung

ableitung von

f (x) = \frac{2 x - 1}{2 x + 1}

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

Schritte zur Lösung

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

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

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

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

Multipliziere aus

2 (2 x + 1) - 2 (2 x - 1) : 4

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

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