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

Lösung

\frac{d}{d x} (\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}}

\frac{d x}{d t} = - \frac{6 x}{20 + 2 t}

\frac{d}{d x} ((3 x^{2} + 1)^{3})

a re a y = x^{3} - 3 x^{2} - x + 3, - 1 < x \leq 3

x \to 1 + lim (\frac{1}{2} x + 3)

x \to - 1 lim (sin (3 x) + 2)