derivative of 2/(sqrt(4x-3))

Lösung

\frac{d}{d x} (\frac{2}{4 x - 3})

- \frac{4}{( 4 x - 3 ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2}{4 x - 3})

Entferne die Konstante:

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

= 2 \frac{d}{d x} (\frac{1}{4 x - 3})

Wende Exponentenregel an:

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

= 2 \frac{d}{d x} ((4 x - 3)^{- \frac{1}{2}})

Wende die Kettenregel an:

- \frac{1}{2 ( 4 x - 3 ) ^{\frac{3}{2}}} \frac{d}{d x} (4 x - 3)

= - \frac{1}{2 ( 4 x - 3 ) ^{\frac{3}{2}}} \frac{d}{d x} (4 x - 3)

\frac{d}{d x} (4 x - 3) = 4

= 2 (- \frac{1}{2 ( 4 x - 3 ) ^{\frac{3}{2}}} \cdot 4)

Vereinfache

2 (- \frac{1}{2 ( 4 x - 3 ) ^{\frac{3}{2}}} \cdot 4) : - \frac{4}{( 4 x - 3 ) ^{\frac{3}{2}}}

= - \frac{4}{( 4 x - 3 ) ^{\frac{3}{2}}}

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