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Beliebt Rechnen >

(\partial)/(\partial y)(x/(x+y))

Lösung

\frac{\partial}{\partial y} (\frac{x}{x + y})

Lösung

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

Schritte zur Lösung

\frac{\partial}{\partial y} (\frac{x}{x + y})

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Beliebte Beispiele

(\partial)/(\partial y)(-1/4 (y^2+x^2))

\frac{\partial}{\partial y} (- \frac{1}{4} (y^{2} + x^{2}))

limit as x approaches-5 of (x+3)/(x+5)

x \to - 5 lim (\frac{x + 3}{x + 5})

integral of 3cos^2(t)

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\frac{d ^{2} y}{d x ^{2}} + 9 y = 0

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