derivative of (12x/(x^2-4))

Lösung

\frac{d}{d x} (\frac{12 x}{x ^{2} - 4})

\frac{12 ( - x ^{2} - 4 )}{( x ^{2} - 4 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{12 x}{x ^{2} - 4})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 12 \frac{d}{d x} (\frac{x}{x ^{2} - 4})

Wende die Quotientenregel an:

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

= 12 \cdot \frac{\frac{d x}{d x} ( x ^{2} - 4 ) - \frac{d}{d x} ( x ^{2} - 4 ) x}{( x ^{2} - 4 ) ^{2}}

\frac{d x}{d x} = 1

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

= 12 \cdot \frac{1 \cdot ( x ^{2} - 4 ) - 2 xx}{( x ^{2} - 4 ) ^{2}}

Vereinfache

12 \cdot \frac{1 \cdot ( x ^{2} - 4 ) - 2 xx}{( x ^{2} - 4 ) ^{2}} : \frac{12 ( - x ^{2} - 4 )}{( x ^{2} - 4 ) ^{2}}

= \frac{12 ( - x ^{2} - 4 )}{( x ^{2} - 4 ) ^{2}}