derivative (-4x)/((x^2-1)^2)

Lösung

ableitung von

\frac{- 4 x}{( x ^{2} - 1 ) ^{2}}

- \frac{4 ( - 3 x ^{2} - 1 )}{( x ^{2} - 1 ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{- 4 x}{( x ^{2} - 1 ) ^{2}})

Vereinfache

\frac{- 4 x}{( x ^{2} - 1 ) ^{2}} : - \frac{4 x}{( x ^{2} - 1 ) ^{2}}

= \frac{d}{d x} (- \frac{4 x}{( x ^{2} - 1 ) ^{2}})

Entferne die Konstante:

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

= - 4 \frac{d}{d x} (\frac{x}{( x ^{2} - 1 ) ^{2}})

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} ((x^{2} - 1)^{2}) = 4 x (x^{2} - 1)

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

Vereinfache

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

= - \frac{4 ( - 3 x ^{2} - 1 )}{( x ^{2} - 1 ) ^{3}}

t an g e n t y = \frac{x}{1 + x ^{2}}, (2, \frac{2}{5})

t an g e n t f (x) = x + 3

\frac{d y}{d t} = (3 - 2 y) \cdot t^{3}

\frac{\partial}{\partial z} (- 5 z)

y^{^{'}} = 8 y