(\partial)/(\partial x)(1/(2x+1))

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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