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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Vereinfache

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

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

= - \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

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

Vereinfache

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

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

Beliebte Beispiele

laplacetransform e^{-3t}+3+2t+4t^2+5t^3

l a pl a ce t r an s f or m e^{- 3 t} + 3 + 2 t + 4 t^{2} + 5 t^{3}

derivative of sin(2x+cos(x))

\frac{d}{d x} (sin (2 x) + cos (x))

integral of cos(x/(sqrt(2)))

\int cos (\frac{x}{2}) d x

(1 + x) d y - y d x = 0

limit as x approaches infinity of 6^x

x \to \infty lim (6^{x})