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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

d er i v a t i v e y^{\frac{2}{3}}

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