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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Vereinfache

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

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

= - \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

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

Vereinfache

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

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

Beliebte Beispiele

(\partial)/(\partial x)(e^{(4xy)})

\frac{\partial}{\partial x} (e^{(4 x y)})

derivative y=xlog_{e}(x)

d er i v a t i v e y = x lo g_{e} (x)

limit as x approaches 4 of-2x^2+4x-4

x \to 4 lim (- 2 x^{2} + 4 x - 4)

3(dy)/(dx)+8/(xy^2)=0

3 \frac{d y}{d x} + \frac{8}{x y ^{2}} = 0

derivative of 2/(x+5)

\frac{d}{d x} (\frac{2}{x + 5})