de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

(\partial)/(\partial z)((x-y)/(x+z))

Lösung

\frac{\partial}{\partial z} (\frac{x - y}{x + z})

Lösung

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

Schritte zur Lösung

\frac{\partial}{\partial z} (\frac{x - y}{x + z})

Behandle

x, y

als Konstanten

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Beliebte Beispiele

y^{''}-2y^'+y=(e^t)/(1+t^2)

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{t}}{1 + t ^{2}}

integral from 0 to pi of sin^4(3x)

\int_{0}^{π} sin^{4} (3 x) d x

\int - 1 d x

(\partial)/(\partial x)(cos(2x-3y))

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

integral of cos(x)*sin(2x)

\int cos (x) \cdot sin (2 x) d x