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Beliebt Rechnen >

(\partial)/(\partial x)(5/(x^2+y^2))

Lösung

\frac{\partial}{\partial x} (\frac{5}{x ^{2} + y ^{2}})

Lösung

- \frac{10 x}{( x ^{2} + y ^{2} ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{5}{x ^{2} + y ^{2}})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 5 \frac{\partial}{\partial x} (\frac{1}{x ^{2} + y ^{2}})

Wende Exponentenregel an:

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

= 5 \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

= 5 (- \frac{1}{( x ^{2} + y ^{2} ) ^{2}} \cdot 2 x)

Vereinfache

5 (- \frac{1}{( x ^{2} + y ^{2} ) ^{2}} \cdot 2 x) : - \frac{10 x}{( x ^{2} + y ^{2} ) ^{2}}

= - \frac{10 x}{( x ^{2} + y ^{2} ) ^{2}}

Beliebte Beispiele

integral from 0 to pi/2 of e^tcos(3t)

\int_{0}^{\frac{π}{2}} e^{t} cos (3 t) d t

limit as x approaches 3 of 4/(x-3)

x \to 3 lim (\frac{4}{x - 3})

derivative f(x)=3(x-2)^2

d er i v a t i v e f (x) = 3 (x - 2)^{2}

xy^'+y=x^4y^4,y(1)= 1/2

x y^{^{'}} + y = x^{4} y^{4}, y (1) = \frac{1}{2}

derivative y=e^{-mx}

d er i v a t i v e y = e^{- m x}