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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Beliebte Beispiele

limit as x approaches 0+of cos(x)-1

x \to 0 + lim (cos (x) - 1)

integral of 2sec(x)tan(x)

\int 2 sec (x) tan (x) d x

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\int \frac{4 x ^{2}}{( x - 2 ) ^{3}} d x

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\frac{d}{d x} (\frac{1}{2} cos^{2} (x))

tangent f(x)= 3/(x^{1/2)}

t an g e n t f (x) = \frac{3}{x ^{\frac{1}{2}}}