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Beliebt Rechnen >

derivative of (45/(0.01x^2+1))

Lösung

\frac{d}{d x} (\frac{45}{0.01 x ^{2} + 1})

Lösung

- \frac{0.9 x}{( 0.01 x ^{2} + 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{45}{0.01 x ^{2} + 1})

Entferne die Konstante:

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

= 45 \frac{d}{d x} (\frac{1}{0.01 x ^{2} + 1})

Wende Exponentenregel an:

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

= 45 \frac{d}{d x} ((0.01 x^{2} + 1)^{- 1})

Wende die Kettenregel an:

- \frac{1}{( 0.01 x ^{2} + 1 ) ^{2}} \frac{d}{d x} (0.01 x^{2} + 1)

= - \frac{1}{( 0.01 x ^{2} + 1 ) ^{2}} \frac{d}{d x} (0.01 x^{2} + 1)

\frac{d}{d x} (0.01 x^{2} + 1) = 0.02 x

= 45 (- \frac{1}{( 0.01 x ^{2} + 1 ) ^{2}} \cdot 0.02 x)

Vereinfache

45 (- \frac{1}{( 0.01 x ^{2} + 1 ) ^{2}} \cdot 0.02 x) : - \frac{0.9 x}{( 0.01 x ^{2} + 1 ) ^{2}}

= - \frac{0.9 x}{( 0.01 x ^{2} + 1 ) ^{2}}

Graph

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