de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative of (ax+b/(ax-b))

Lösung

\frac{d}{d x} (\frac{a x + b}{a x - b})

Lösung

- \frac{2 ab}{( a x - b ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{a x + b}{a x - b})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( a x + b ) ( a x - b ) - \frac{d}{d x} ( a x - b ) ( a x + b )}{( a x - b ) ^{2}}

\frac{d}{d x} (a x + b) = a

\frac{d}{d x} (a x - b) = a

= \frac{a ( a x - b ) - a ( a x + b )}{( a x - b ) ^{2}}

Vereinfache

\frac{a ( a x - b ) - a ( a x + b )}{( a x - b ) ^{2}} : - \frac{2 ab}{( a x - b ) ^{2}}

= - \frac{2 ab}{( a x - b ) ^{2}}

Graph

Beliebte Beispiele

tangent f(x)=x^2+4,(3,13)

t an g e n t f (x) = x^{2} + 4, (3, 13)

integral of e^{-x}

\int e^{- x} d x

(\partial)/(\partial x)(ln(2))

\frac{\partial}{\partial x} (ln (2))

fläche 32-2x^2,[0,7]

a re a 32 - 2 x^{2}, [0, 7]

limit as x approaches 0 of ((x^3))/(tan^3(2x))

x \to 0 lim (\frac{( x ^{3} )}{tan ^{3} ( 2 x )})