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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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