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Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{36 y x}{( 9 x ^{2} + y ^{2} + 9 ) ^{2}}

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial x} (9 x^{2} + y^{2} + 9) = 18 x

= 2 y (- \frac{1}{( 9 x ^{2} + y ^{2} + 9 ) ^{2}} \cdot 18 x)

Vereinfache

2 y (- \frac{1}{( 9 x ^{2} + y ^{2} + 9 ) ^{2}} \cdot 18 x) : - \frac{36 y x}{( 9 x ^{2} + y ^{2} + 9 ) ^{2}}

= - \frac{36 y x}{( 9 x ^{2} + y ^{2} + 9 ) ^{2}}

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