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Beliebt Rechnen >

derivative of (10/(x^2+1))

Lösung

\frac{d}{d x} (\frac{10}{x ^{2} + 1})

Lösung

- \frac{20 x}{( x ^{2} + 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{10}{x ^{2} + 1})

Entferne die Konstante:

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

= 10 \frac{d}{d x} (\frac{1}{x ^{2} + 1})

Wende Exponentenregel an:

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

= 10 \frac{d}{d x} ((x^{2} + 1)^{- 1})

Wende die Kettenregel an:

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

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

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

= 10 (- \frac{1}{( x ^{2} + 1 ) ^{2}} \cdot 2 x)

Vereinfache

10 (- \frac{1}{( x ^{2} + 1 ) ^{2}} \cdot 2 x) : - \frac{20 x}{( x ^{2} + 1 ) ^{2}}

= - \frac{20 x}{( x ^{2} + 1 ) ^{2}}

Graph

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