(\partial)/(\partial x)((x+3)/(x^2-x-2))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{\partial}{\partial x} (x + 3) = 1

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

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

Vereinfache

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

= \frac{- x ^{2} - 6 x + 1}{( x ^{2} - x - 2 ) ^{2}}

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