de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative f(x)=(x^3)/(x^2-1)

Lösung

ableitung von

f (x) = \frac{x ^{3}}{x ^{2} - 1}

Lösung

\frac{x ^{4} - 3 x ^{2}}{( x ^{2} - 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{3}}{x ^{2} - 1})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{3} ) ( x ^{2} - 1 ) - \frac{d}{d x} ( x ^{2} - 1 ) x ^{3}}{( x ^{2} - 1 ) ^{2}}

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

= \frac{3 x ^{2} ( x ^{2} - 1 ) - 2 x x ^{3}}{( x ^{2} - 1 ) ^{2}}

Vereinfache

\frac{3 x ^{2} ( x ^{2} - 1 ) - 2 x x ^{3}}{( x ^{2} - 1 ) ^{2}} : \frac{x ^{4} - 3 x ^{2}}{( x ^{2} - 1 ) ^{2}}

= \frac{x ^{4} - 3 x ^{2}}{( x ^{2} - 1 ) ^{2}}

Graph

Beliebte Beispiele

integral of x/(sqrt(x^2-9))

\int \frac{x}{x ^{2} - 9} d x

derivative of 3^{x^5+2}

\frac{d}{d x} (3^{x^{5} + 2})

(\partial)/(\partial x)(2xsin(xy))

\frac{\partial}{\partial x} (2 x sin (x y))

x v^{'} + 2 v = 0

xy^'=2y+x^3cos(x)

x y^{^{'}} = 2 y + x^{3} cos (x)