derivative of 1/(9+x^2)

Lösung

\frac{d}{d x} (\frac{1}{9 + x ^{2}})

- \frac{2 x}{( 9 + x ^{2} ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{9 + x ^{2}})

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (9 + x^{2}) = 2 x

= - \frac{1}{( 9 + x ^{2} ) ^{2}} \cdot 2 x

Vereinfache

- \frac{1}{( 9 + x ^{2} ) ^{2}} \cdot 2 x : - \frac{2 x}{( 9 + x ^{2} ) ^{2}}

= - \frac{2 x}{( 9 + x ^{2} ) ^{2}}

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