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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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