d/(d{x)}(1/(sqrt(9-{x)^2-{y)^2-{z}^2}})

Lösung

\frac{d}{d x} (\frac{1}{9 - x ^{2} - y ^{2} - z ^{2}})

\frac{x}{( 9 - x ^{2} - y ^{2} - z ^{2} ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{9 - x ^{2} - y ^{2} - z ^{2}})

Wende Exponentenregel an:

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

= \frac{d}{d x} ((9 - x^{2} - y^{2} - z^{2})^{- \frac{1}{2}})

Wende die Kettenregel an:

- \frac{1}{2 ( 9 - x ^{2} - y ^{2} - z ^{2} ) ^{\frac{3}{2}}} \frac{d}{d x} (9 - x^{2} - y^{2} - z^{2})

= - \frac{1}{2 ( 9 - x ^{2} - y ^{2} - z ^{2} ) ^{\frac{3}{2}}} \frac{d}{d x} (9 - x^{2} - y^{2} - z^{2})

\frac{d}{d x} (9 - x^{2} - y^{2} - z^{2}) = - 2 x

= - \frac{1}{2 ( 9 - x ^{2} - y ^{2} - z ^{2} ) ^{\frac{3}{2}}} (- 2 x)

Vereinfache

- \frac{1}{2 ( 9 - x ^{2} - y ^{2} - z ^{2} ) ^{\frac{3}{2}}} (- 2 x) : \frac{x}{( 9 - x ^{2} - y ^{2} - z ^{2} ) ^{\frac{3}{2}}}

= \frac{x}{( 9 - x ^{2} - y ^{2} - z ^{2} ) ^{\frac{3}{2}}}

((x - 1)^{2})^{^{'}}

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\int_{0}^{0.6} \frac{x ^{2}}{9 - 25 x ^{2}} d x