derivative 4/(1+x^2)

Lösung

ableitung von

\frac{4}{1 + x ^{2}}

- \frac{8 x}{( 1 + x ^{2} ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{4}{1 + x ^{2}})

Entferne die Konstante:

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

= 4 \frac{d}{d x} (\frac{1}{1 + x ^{2}})

Wende Exponentenregel an:

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

= 4 \frac{d}{d x} ((1 + x^{2})^{- 1})

Wende die Kettenregel an:

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

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

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

= 4 (- \frac{1}{( 1 + x ^{2} ) ^{2}} \cdot 2 x)

Vereinfache

4 (- \frac{1}{( 1 + x ^{2} ) ^{2}} \cdot 2 x) : - \frac{8 x}{( 1 + x ^{2} ) ^{2}}

= - \frac{8 x}{( 1 + x ^{2} ) ^{2}}

\frac{d}{d x} (\frac{1}{e})

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