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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

= \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

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

Vereinfache

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

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

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

d er i v a t i v e 6 x^{\frac{1}{3}}

d er i v a t i v e \frac{( x + 2 ) ^{2}}{3}

d er i v a t i v e (5 x + 2)^{7}

\frac{d}{d t} (t^{3} + 7 t^{2} + 24 t + 12)