derivative of (-8x/((x^2-16)^2))

Lösung

\frac{d}{d x} (\frac{- 8 x}{( x ^{2} - 16 ) ^{2}})

- \frac{8 ( - 3 x ^{2} - 16 )}{( x ^{2} - 16 ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{- 8 x}{( x ^{2} - 16 ) ^{2}})

Vereinfache

\frac{- 8 x}{( x ^{2} - 16 ) ^{2}} : - \frac{8 x}{( x ^{2} - 16 ) ^{2}}

= \frac{d}{d x} (- \frac{8 x}{( x ^{2} - 16 ) ^{2}})

Entferne die Konstante:

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

= - 8 \frac{d}{d x} (\frac{x}{( x ^{2} - 16 ) ^{2}})

Wende die Quotientenregel an:

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

= - 8 \cdot \frac{\frac{d x}{d x} ( x ^{2} - 16 ) ^{2} - \frac{d}{d x} ( ( x ^{2} - 16 ) ^{2} ) x}{( ( x ^{2} - 16 ) ^{2} ) ^{2}}

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

\frac{d}{d x} ((x^{2} - 16)^{2}) = 4 x (x^{2} - 16)

= - 8 \cdot \frac{1 \cdot ( x ^{2} - 16 ) ^{2} - 4 x ( x ^{2} - 16 ) x}{( ( x ^{2} - 16 ) ^{2} ) ^{2}}

Vereinfache

- 8 \cdot \frac{1 \cdot ( x ^{2} - 16 ) ^{2} - 4 x ( x ^{2} - 16 ) x}{( ( x ^{2} - 16 ) ^{2} ) ^{2}} : - \frac{8 ( - 3 x ^{2} - 16 )}{( x ^{2} - 16 ) ^{3}}

= - \frac{8 ( - 3 x ^{2} - 16 )}{( x ^{2} - 16 ) ^{3}}

\int tan^{5} (x) sec (x) d x

ma c l a u r in 5 e^{- x}

\frac{d}{d x} ((sin (x))^{l n (x)})

\frac{\partial}{\partial x} (x^{2} y + 5 y^{3})

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