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)((26x^2)/((x-y)^2))

Lösung

\frac{\partial}{\partial x} (\frac{26 x ^{2}}{( x - y ) ^{2}})

Lösung

- \frac{52 x y}{( x - y ) ^{3}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{26 x ^{2}}{( x - y ) ^{2}})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 26 \frac{\partial}{\partial x} (\frac{x ^{2}}{( x - y ) ^{2}})

Wende die Quotientenregel an:

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

= 26 \cdot \frac{\frac{\partial}{\partial x} ( x ^{2} ) ( x - y ) ^{2} - \frac{\partial}{\partial x} ( ( x - y ) ^{2} ) x ^{2}}{( ( x - y ) ^{2} ) ^{2}}

\frac{\partial}{\partial x} (x^{2}) = 2 x

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

= 26 \cdot \frac{2 x ( x - y ) ^{2} - 2 ( x - y ) x ^{2}}{( ( x - y ) ^{2} ) ^{2}}

Vereinfache

26 \cdot \frac{2 x ( x - y ) ^{2} - 2 ( x - y ) x ^{2}}{( ( x - y ) ^{2} ) ^{2}} : - \frac{52 x y}{( x - y ) ^{3}}

= - \frac{52 x y}{( x - y ) ^{3}}

Beliebte Beispiele

tangent 1+4x^2-2x^3

t an g e n t 1 + 4 x^{2} - 2 x^{3}

derivative of sqrt(sin(x-1(x^3)))

\frac{d}{d x} (sin (x - 1) (x^{3}))

limit as x approaches 6 of 9

x \to 6 lim (9)

(dy)/(dt)+t^2y=1

\frac{d y}{d t} + t^{2} y = 1

(\partial)/(\partial x)(e^xcos(y))

\frac{\partial}{\partial x} (e^{x} cos (y))