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)((x+y)/(xy-1))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

Beliebte Beispiele

(dy)/(dx)=sin(y)+1

\frac{d y}{d x} = sin (y) + 1

derivative of x^{3cos(x})

\frac{d}{d x} (x^{3 c o s (x)})

limit as x approaches 8 of (1+\sqrt[3]{x})(x^3-6x^2+2)

x \to 8 lim ((1 + 3 x) (x^{3} - 6 x^{2} + 2))

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

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

derivative f(x)=4x^2-x^3

d er i v a t i v e f (x) = 4 x^{2} - x^{3}