derivative of 1/(sqrt(1+2x))

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

= \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}}}

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