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}})

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}}

x \to 0 + lim (x^{2} - 2 x - 3)

\frac{\partial}{\partial x} (2 + y ln (4 + x y^{2}))

d er i v a t i v e x (x^{2} + 4)

d er i v a t i v e \frac{( x ^{2} - 1 )}{x ^{2} + 1}

\int_{- \infty}^{0} \frac{z}{z ^{4} + 4} d z