derivative 1/(1+9x^2)

Lösung

ableitung von

\frac{1}{1 + 9 x ^{2}}

- \frac{18 x}{( 1 + 9 x ^{2} ) ^{2}}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (1 + 9 x^{2}) = 18 x

= - \frac{1}{( 1 + 9 x ^{2} ) ^{2}} \cdot 18 x

Vereinfache

- \frac{1}{( 1 + 9 x ^{2} ) ^{2}} \cdot 18 x : - \frac{18 x}{( 1 + 9 x ^{2} ) ^{2}}

= - \frac{18 x}{( 1 + 9 x ^{2} ) ^{2}}

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