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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

x \to - 5 + lim (\frac{2}{x ^{2} - 25})

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