derivative of-(2x/((4+x^2)^2))

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\int \frac{x ^{2} + x - 3}{x} d x

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

\int \frac{1}{( 1 + 2 x )} d x

y^{^{''}} - 3 y^{^{'}} - 10 y = - 4 e^{4 t}, y (0) = 0, y^{^{'}} (0) = 0

\int 12 e^{4 x} d x