de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Beliebte Beispiele

integral of (x^2)

\int (x^{2}) d x

derivative of (2x^{2x})

\frac{d}{d x} ((2 x)^{2 x})

derivative of 4x^3sec(7x)

\frac{d}{d x} (4 x^{3} sec (7 x))

tangent sqrt(x^2+16),\at x=3

t an g e n t x^{2} + 16, at x = 3

integral of 1/3 x^3sqrt(9-x^2)

\int \frac{1}{3} x^{3} 9 - x^{2} d x