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Beliebt Rechnen >

derivative of (2x-1^{1/2})

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

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