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)((61)/(7+x^2+y^2))

Lösung

\frac{\partial}{\partial x} (\frac{61}{7 + x ^{2} + y ^{2}})

Lösung

- \frac{122 x}{( 7 + x ^{2} + y ^{2} ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{61}{7 + x ^{2} + y ^{2}})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 61 \frac{\partial}{\partial x} (\frac{1}{7 + x ^{2} + y ^{2}})

Wende Exponentenregel an:

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

= 61 \frac{\partial}{\partial x} ((7 + x^{2} + y^{2})^{- 1})

Wende die Kettenregel an:

- \frac{1}{( 7 + x ^{2} + y ^{2} ) ^{2}} \frac{\partial}{\partial x} (7 + x^{2} + y^{2})

= - \frac{1}{( 7 + x ^{2} + y ^{2} ) ^{2}} \frac{\partial}{\partial x} (7 + x^{2} + y^{2})

\frac{\partial}{\partial x} (7 + x^{2} + y^{2}) = 2 x

= 61 (- \frac{1}{( 7 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x)

Vereinfache

61 (- \frac{1}{( 7 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x) : - \frac{122 x}{( 7 + x ^{2} + y ^{2} ) ^{2}}

= - \frac{122 x}{( 7 + x ^{2} + y ^{2} ) ^{2}}

Beliebte Beispiele

limit as x approaches 3 of (x^2+1)/(x-3)

x \to 3 lim (\frac{x ^{2} + 1}{x - 3})

derivative of sin(x^2+5)

\frac{d}{d x} (sin (x^{2} + 5))

derivative of (7x/(e^x))

\frac{d}{d x} (\frac{7 x}{e ^{x}})

sum from n=1 to infinity of 9/(10^n)

n = 1 \sum \infty \frac{9}{1 0 ^{n}}

d/(dt)(cos(3t))

\frac{d}{d t} (cos (3 t))