derivative g(x)= 3/(sqrt(6x+8))

Lösung

ableitung von

g (x) = \frac{3}{6 x + 8}

- \frac{9}{( 6 x + 8 ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3}{6 x + 8})

Entferne die Konstante:

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

= 3 \frac{d}{d x} (\frac{1}{6 x + 8})

Wende Exponentenregel an:

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

= 3 \frac{d}{d x} ((6 x + 8)^{- \frac{1}{2}})

Wende die Kettenregel an:

- \frac{1}{2 ( 6 x + 8 ) ^{\frac{3}{2}}} \frac{d}{d x} (6 x + 8)

= - \frac{1}{2 ( 6 x + 8 ) ^{\frac{3}{2}}} \frac{d}{d x} (6 x + 8)

\frac{d}{d x} (6 x + 8) = 6

= 3 (- \frac{1}{2 ( 6 x + 8 ) ^{\frac{3}{2}}} \cdot 6)

Vereinfache

3 (- \frac{1}{2 ( 6 x + 8 ) ^{\frac{3}{2}}} \cdot 6) : - \frac{9}{( 6 x + 8 ) ^{\frac{3}{2}}}

= - \frac{9}{( 6 x + 8 ) ^{\frac{3}{2}}}

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