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)((8x)/(x^2+6y^2))

Lösung

\frac{\partial}{\partial x} (\frac{8 x}{x ^{2} + 6 y ^{2}})

Lösung

\frac{8 ( - x ^{2} + 6 y ^{2} )}{( x ^{2} + 6 y ^{2} ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{8 x}{x ^{2} + 6 y ^{2}})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 8 \frac{\partial}{\partial x} (\frac{x}{x ^{2} + 6 y ^{2}})

Wende die Quotientenregel an:

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

= 8 \cdot \frac{\frac{\partial}{\partial x} ( x ) ( x ^{2} + 6 y ^{2} ) - \frac{\partial}{\partial x} ( x ^{2} + 6 y ^{2} ) x}{( x ^{2} + 6 y ^{2} ) ^{2}}

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

\frac{\partial}{\partial x} (x^{2} + 6 y^{2}) = 2 x

= 8 \cdot \frac{1 \cdot ( x ^{2} + 6 y ^{2} ) - 2 xx}{( x ^{2} + 6 y ^{2} ) ^{2}}

Vereinfache

8 \cdot \frac{1 \cdot ( x ^{2} + 6 y ^{2} ) - 2 xx}{( x ^{2} + 6 y ^{2} ) ^{2}} : \frac{8 ( - x ^{2} + 6 y ^{2} )}{( x ^{2} + 6 y ^{2} ) ^{2}}

= \frac{8 ( - x ^{2} + 6 y ^{2} )}{( x ^{2} + 6 y ^{2} ) ^{2}}

Beliebte Beispiele

limit as x approaches 0 of (sqrt(9+x))/x

x \to 0 lim (\frac{9 + x}{x})

derivative ln(\sqrt[5]{x})

d er i v a t i v e ln (5 x)

integral of (e^{2x})/(2-e^{2x)}

\int \frac{e ^{2 x}}{2 - e ^{2 x}} d x

y^{''}-1/t y^'+2/(t^2)y=0

y^{^{''}} - \frac{1}{t} y^{^{'}} + \frac{2}{t ^{2}} y = 0

integral of xsqrt(4-3x^2)

\int x 4 - 3 x^{2} d x