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Beliebt Rechnen >

(\partial)/(\partial x)(1/(7+5x))

Lösung

\frac{\partial}{\partial x} (\frac{1}{7 + 5 x})

Lösung

- \frac{5}{( 7 + 5 x ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{1}{7 + 5 x})

Wende Exponentenregel an:

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

= \frac{\partial}{\partial x} ((7 + 5 x)^{- 1})

Wende die Kettenregel an:

- \frac{1}{( 7 + 5 x ) ^{2}} \frac{\partial}{\partial x} (7 + 5 x)

= - \frac{1}{( 7 + 5 x ) ^{2}} \frac{\partial}{\partial x} (7 + 5 x)

\frac{\partial}{\partial x} (7 + 5 x) = 5

= - \frac{1}{( 7 + 5 x ) ^{2}} \cdot 5

Vereinfache

- \frac{1}{( 7 + 5 x ) ^{2}} \cdot 5 : - \frac{5}{( 7 + 5 x ) ^{2}}

= - \frac{5}{( 7 + 5 x ) ^{2}}

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