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}}

y^{^{''}} = - y + 0.1 y^{^{'}}

x \to 0 lim (81 x^{4} - 216 x^{3} + 216 x^{2} - 96 x + 16)

y^{^{'}} - y = 11 t e^{2 t}

n \to \infty lim (\frac{1}{4 n})

\int e^{\frac{- x}{4}} d x