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Beliebt Rechnen >

(\partial)/(\partial x)(((2+t^2))/(3x-x^3))

Lösung

\frac{\partial}{\partial x} (\frac{( 2 + t ^{2} )}{3 x - x ^{3}})

Lösung

- \frac{( 2 + t ^{2} ) ( 3 - 3 x ^{2} )}{( 3 x - x ^{3} ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{( 2 + t ^{2} )}{3 x - x ^{3}})

Behandle

t

als Konstante

Entferne die Konstante:

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

= (2 + t^{2}) \frac{\partial}{\partial x} (\frac{1}{3 x - x ^{3}})

Wende Exponentenregel an:

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

= (2 + t^{2}) \frac{\partial}{\partial x} ((3 x - x^{3})^{- 1})

Wende die Kettenregel an:

- \frac{1}{( 3 x - x ^{3} ) ^{2}} \frac{\partial}{\partial x} (3 x - x^{3})

= - \frac{1}{( 3 x - x ^{3} ) ^{2}} \frac{\partial}{\partial x} (3 x - x^{3})

\frac{\partial}{\partial x} (3 x - x^{3}) = 3 - 3 x^{2}

= (2 + t^{2}) (- \frac{1}{( 3 x - x ^{3} ) ^{2}} (3 - 3 x^{2}))

Vereinfache

(2 + t^{2}) (- \frac{1}{( 3 x - x ^{3} ) ^{2}} (3 - 3 x^{2})) : - \frac{( 2 + t ^{2} ) ( 3 - 3 x ^{2} )}{( 3 x - x ^{3} ) ^{2}}

= - \frac{( 2 + t ^{2} ) ( 3 - 3 x ^{2} )}{( 3 x - x ^{3} ) ^{2}}

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