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Beliebt Rechnen >

derivative of 2/((3x^2+7^2))

Lösung

\frac{d}{d x} (\frac{2}{( 3 x ^{2} + 7 ) ^{2}})

Lösung

- \frac{24 x}{( 3 x ^{2} + 7 ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2}{( 3 x ^{2} + 7 ) ^{2}})

Entferne die Konstante:

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

= 2 \frac{d}{d x} (\frac{1}{( 3 x ^{2} + 7 ) ^{2}})

Wende Exponentenregel an:

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

= 2 \frac{d}{d x} ((3 x^{2} + 7)^{- 2})

Wende die Kettenregel an:

- \frac{2}{( 3 x ^{2} + 7 ) ^{3}} \frac{d}{d x} (3 x^{2} + 7)

= - \frac{2}{( 3 x ^{2} + 7 ) ^{3}} \frac{d}{d x} (3 x^{2} + 7)

\frac{d}{d x} (3 x^{2} + 7) = 6 x

= 2 (- \frac{2}{( 3 x ^{2} + 7 ) ^{3}} \cdot 6 x)

Vereinfache

2 (- \frac{2}{( 3 x ^{2} + 7 ) ^{3}} \cdot 6 x) : - \frac{24 x}{( 3 x ^{2} + 7 ) ^{3}}

= - \frac{24 x}{( 3 x ^{2} + 7 ) ^{3}}

Graph

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\int \frac{3}{t ^{2}} d t