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Beliebt Rechnen >

derivative of (75/(sqrt(12+x^2+y^2)))

Lösung

\frac{d}{d x} (\frac{75}{12 + x ^{2} + y ^{2}})

Lösung

- \frac{75 ( x + y \frac{d y}{d x} )}{( 12 + x ^{2} + y ^{2} ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{75}{12 + x ^{2} + y ^{2}})

Entferne die Konstante:

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

= 75 \frac{d}{d x} (\frac{1}{12 + x ^{2} + y ^{2}})

Wende Exponentenregel an:

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

= 75 \frac{d}{d x} ((12 + x^{2} + y^{2})^{- \frac{1}{2}})

Wende die Kettenregel an:

- \frac{1}{2 ( 12 + x ^{2} + y ^{2} ) ^{\frac{3}{2}}} \frac{d}{d x} (12 + x^{2} + y^{2})

= - \frac{1}{2 ( 12 + x ^{2} + y ^{2} ) ^{\frac{3}{2}}} \frac{d}{d x} (12 + x^{2} + y^{2})

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

= 75 (- \frac{1}{2 ( 12 + x ^{2} + y ^{2} ) ^{\frac{3}{2}}} (2 x + 2 y \frac{d y}{d x}))

Vereinfache

75 (- \frac{1}{2 ( 12 + x ^{2} + y ^{2} ) ^{\frac{3}{2}}} (2 x + 2 y \frac{d y}{d x})) : - \frac{75 ( x + y \frac{d y}{d x} )}{( 12 + x ^{2} + y ^{2} ) ^{\frac{3}{2}}}

= - \frac{75 ( x + y \frac{d y}{d x} )}{( 12 + x ^{2} + y ^{2} ) ^{\frac{3}{2}}}

Beliebte Beispiele

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