de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Vereinfache

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

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

- \frac{2}{( x + y ) ^{3}} \frac{\partial}{\partial y} (x + y)

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

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

= - x (- \frac{2}{( x + y ) ^{3}} \cdot 1)

Vereinfache

- x (- \frac{2}{( x + y ) ^{3}} \cdot 1) : \frac{2 x}{( x + y ) ^{3}}

= \frac{2 x}{( x + y ) ^{3}}

Beliebte Beispiele

integral from 0 to 1 of xsqrt(8-x^2)

\int_{0}^{1} x 8 - x^{2} d x

(1+ln(x)+y/x)dx=(7-ln(x))dy

(1 + ln (x) + \frac{y}{x}) d x = (7 - ln (x)) d y

limit as x approaches-7 of sqrt(1/(x+7))

x \to - 7 lim (\frac{1}{x + 7})

laplacetransform [t]

l a pl a ce t r an s f or m [t]

derivative of ln(e^{6x})

\frac{d}{d x} (ln (e^{6 x}))