derivative y= 1/(sqrt(2x-1))

Lösung

ableitung von

y = \frac{1}{2 x - 1}

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

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{2 x - 1})

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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