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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

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\int (cos (θ) sin (θ)) d θ

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