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Beliebt Rechnen >

d/(dy)((350)/(sqrt(x^2+y^2)))

Lösung

\frac{d}{d y} (\frac{350}{x ^{2} + y ^{2}})

Lösung

- \frac{350 y}{( x ^{2} + y ^{2} ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d y} (\frac{350}{x ^{2} + y ^{2}})

Behandle

x

als Konstante

Entferne die Konstante:

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

= 350 \frac{d}{d y} (\frac{1}{x ^{2} + y ^{2}})

Wende Exponentenregel an:

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

= 350 \frac{d}{d y} ((x^{2} + y^{2})^{- \frac{1}{2}})

Wende die Kettenregel an:

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

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

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

= 350 (- \frac{1}{2 ( x ^{2} + y ^{2} ) ^{\frac{3}{2}}} \cdot 2 y)

Vereinfache

350 (- \frac{1}{2 ( x ^{2} + y ^{2} ) ^{\frac{3}{2}}} \cdot 2 y) : - \frac{350 y}{( x ^{2} + y ^{2} ) ^{\frac{3}{2}}}

= - \frac{350 y}{( x ^{2} + y ^{2} ) ^{\frac{3}{2}}}

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