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Beliebt Rechnen >

(\partial)/(\partial x)((100)/(6x^2+y^2))

Lösung

\frac{\partial}{\partial x} (\frac{100}{6 x ^{2} + y ^{2}})

Lösung

- \frac{1200 x}{( 6 x ^{2} + y ^{2} ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{100}{6 x ^{2} + y ^{2}})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 100 \frac{\partial}{\partial x} (\frac{1}{6 x ^{2} + y ^{2}})

Wende Exponentenregel an:

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

= 100 \frac{\partial}{\partial x} ((6 x^{2} + y^{2})^{- 1})

Wende die Kettenregel an:

- \frac{1}{( 6 x ^{2} + y ^{2} ) ^{2}} \frac{\partial}{\partial x} (6 x^{2} + y^{2})

= - \frac{1}{( 6 x ^{2} + y ^{2} ) ^{2}} \frac{\partial}{\partial x} (6 x^{2} + y^{2})

\frac{\partial}{\partial x} (6 x^{2} + y^{2}) = 12 x

= 100 (- \frac{1}{( 6 x ^{2} + y ^{2} ) ^{2}} \cdot 12 x)

Vereinfache

100 (- \frac{1}{( 6 x ^{2} + y ^{2} ) ^{2}} \cdot 12 x) : - \frac{1200 x}{( 6 x ^{2} + y ^{2} ) ^{2}}

= - \frac{1200 x}{( 6 x ^{2} + y ^{2} ) ^{2}}

Beliebte Beispiele

derivative 1/(\sqrt[3]{x)}

d er i v a t i v e \frac{1}{3 x}

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\int \frac{- x ^{3} + 2 x ^{2} - x - 1}{x ^{3} + x} d x

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\int_{- 1}^{3} 3 x^{2} d x

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