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Beliebt Rechnen >

derivative of 4/(x^2+2)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

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