derivative (-x^2-8)/((x^2-8)^2)

Lösung

ableitung von

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

- \frac{2 x ( - x ^{2} - 24 )}{( x ^{2} - 8 ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{- x ^{2} - 8}{( x ^{2} - 8 ) ^{2}})

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{( - 2 x ) ( x ^{2} - 8 ) ^{2} - 4 x ( x ^{2} - 8 ) ( - x ^{2} - 8 )}{( ( x ^{2} - 8 ) ^{2} ) ^{2}} : - \frac{2 x ( - x ^{2} - 24 )}{( x ^{2} - 8 ) ^{3}}

= - \frac{2 x ( - x ^{2} - 24 )}{( x ^{2} - 8 ) ^{3}}

\int_{\frac{1}{3}}^{5} 14 x ln (3 x) d x

in v erse l a pl a ce \frac{( e ^{- s} )}{s ^{2} - 6 s + 9}

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