derivative of (-x^2/(2x^2-3))

Lösung

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

\frac{6 x}{( 2 x ^{2} - 3 ) ^{2}}

Schritte zur Lösung

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

Vereinfache

\frac{- x ^{2}}{2 x ^{2} - 3} : - \frac{x ^{2}}{2 x ^{2} - 3}

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (2 x^{2} - 3) = 4 x

= - \frac{2 x ( 2 x ^{2} - 3 ) - 4 x x ^{2}}{( 2 x ^{2} - 3 ) ^{2}}

Vereinfache

- \frac{2 x ( 2 x ^{2} - 3 ) - 4 x x ^{2}}{( 2 x ^{2} - 3 ) ^{2}} : \frac{6 x}{( 2 x ^{2} - 3 ) ^{2}}

= \frac{6 x}{( 2 x ^{2} - 3 ) ^{2}}