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

Lösung

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

\frac{x ^{2} - 8 x + 4}{( - x ^{2} + 4 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (x - 4) = 1

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

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

Vereinfache

\frac{1 \cdot ( - x ^{2} + 4 ) - ( - 2 x ) ( x - 4 )}{( - x ^{2} + 4 ) ^{2}} : \frac{x ^{2} - 8 x + 4}{( - x ^{2} + 4 ) ^{2}}

= \frac{x ^{2} - 8 x + 4}{( - x ^{2} + 4 ) ^{2}}