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

Lösung

ableitung von

y = \frac{x + 1}{2 x - 1}

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

y^{^{'}} - y = e^{2 x}

\int 12 cos (4 x) d x

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