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Beliebt Rechnen >

(\partial)/(\partial x)((63)/((9+x^2+y^2)))

Lösung

\frac{\partial}{\partial x} (\frac{63}{( 9 + x ^{2} + y ^{2} )})

Lösung

- \frac{126 x}{( 9 + x ^{2} + y ^{2} ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{63}{( 9 + x ^{2} + y ^{2} )})

Behandle

y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 63 \frac{\partial}{\partial x} (\frac{1}{9 + x ^{2} + y ^{2}})

Wende Exponentenregel an:

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

= 63 \frac{\partial}{\partial x} ((9 + x^{2} + y^{2})^{- 1})

Wende die Kettenregel an:

- \frac{1}{( 9 + x ^{2} + y ^{2} ) ^{2}} \frac{\partial}{\partial x} (9 + x^{2} + y^{2})

= - \frac{1}{( 9 + x ^{2} + y ^{2} ) ^{2}} \frac{\partial}{\partial x} (9 + x^{2} + y^{2})

\frac{\partial}{\partial x} (9 + x^{2} + y^{2}) = 2 x

= 63 (- \frac{1}{( 9 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x)

Vereinfache

63 (- \frac{1}{( 9 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x) : - \frac{126 x}{( 9 + x ^{2} + y ^{2} ) ^{2}}

= - \frac{126 x}{( 9 + x ^{2} + y ^{2} ) ^{2}}

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