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

Lösung

ableitung von

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int cos (t) d t

\int_{- 64}^{64} \frac{1}{x ^{\frac{1}{3}}} d x

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

d er i v a t i v e 3 1 + 7 x

in v erse l a pl a ce \frac{1}{s ( s ^{2} - 2 s + 2 )}