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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (\frac{1 - cos ( x )}{x})

\int \frac{2 x - 1}{2 x + 3} d x

\frac{d}{d x} (ln (x + 2 y + 3 z))

y^{^{'''}} = e^{- 0.2 x}

in v erse l a pl a ce \frac{( s + 2 )}{( s ^{2} + 4 )}