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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} ((x^{2} + 2 x)^{5})

a re a y = x^{2}, y = x, y = 2

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

n = 0 \sum \infty (\frac{1}{2})^{2 n}

d er i v a t i v e y = \frac{1}{3} e^{3 x}