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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Beliebte Beispiele

(\partial)/(\partial v)(u^2)

\frac{\partial}{\partial v} (u^{2})

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

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

x y^{^{'}} + 2 y = - 4 x

derivative of (x^3^5)

\frac{d}{d x} ((x^{3})^{5})

sum from n=0 to infinity of 1+1/n

n = 0 \sum \infty 1 + \frac{1}{n}