derivative of 2/(1-x^2)

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int \frac{1}{2 x - 1} d x

\frac{d}{d x} (\frac{5 1 - x ^{3}}{6})

\int 13 arctan (x) d x

x \to + 0 lim (\frac{e ^{2 x} - 1}{sin ( 3 x )})

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