de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{\partial}{\partial x} (x) = 1

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

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

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

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

Beliebte Beispiele

integral of 5cos(x)-4sin(x)

\int 5 cos (x) - 4 sin (x) d x

derivative y=\sqrt[4]{(cos(x))^3}

d er i v a t i v e y = 4 (cos (x))^{3}

derivative of (2x+3^2)

\frac{d}{d x} ((2 x + 3)^{2})

derivative f(x)=a^4+cos^4(x)

d er i v a t i v e f (x) = a^{4} + cos^{4} (x)

integral from 0 to 1 of 2pi(2-y)(4y^2)

\int_{0}^{1} 2 π (2 - y) (4 y^{2}) d y