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Beliebt Rechnen >

derivative of 3/((8x+3^2))

Lösung

\frac{d}{d x} (\frac{3}{( 8 x + 3 ) ^{2}})

Lösung

- \frac{48}{( 8 x + 3 ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3}{( 8 x + 3 ) ^{2}})

Entferne die Konstante:

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

= 3 \frac{d}{d x} (\frac{1}{( 8 x + 3 ) ^{2}})

Wende Exponentenregel an:

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

= 3 \frac{d}{d x} ((8 x + 3)^{- 2})

Wende die Kettenregel an:

- \frac{2}{( 8 x + 3 ) ^{3}} \frac{d}{d x} (8 x + 3)

= - \frac{2}{( 8 x + 3 ) ^{3}} \frac{d}{d x} (8 x + 3)

\frac{d}{d x} (8 x + 3) = 8

= 3 (- \frac{2}{( 8 x + 3 ) ^{3}} \cdot 8)

Vereinfache

3 (- \frac{2}{( 8 x + 3 ) ^{3}} \cdot 8) : - \frac{48}{( 8 x + 3 ) ^{3}}

= - \frac{48}{( 8 x + 3 ) ^{3}}

Graph

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