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Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{2}{x ^{3}}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial x} (\frac{1}{x ^{2}}) = - \frac{2}{x ^{3}}

\frac{\partial}{\partial x} (\frac{1}{y ^{2}}) = 0

= - \frac{2}{x ^{3}} + 0

Vereinfache

= - \frac{2}{x ^{3}}

Beliebte Beispiele

derivative of cotan(3-2x)

\frac{d}{d x} (co tan (3 - 2 x))

limit as x approaches-2+of x

x \to - 2 + lim (x)

derivative of (sin(2x+1)/(2x+1))

\frac{d}{d x} (\frac{sin ( 2 x + 1 )}{2 x + 1})

integral of-x^{-4}

\int - x^{- 4} d x

integral of t^4

\int t^{4} d t