de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative (x^2)/(2-x^2)

Lösung

ableitung von

\frac{x ^{2}}{2 - x ^{2}}

Lösung

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of xsin(-1x)

\int x sin (- 1 x) d x

integral of e^{-sqrt(y)}

\int e^{- y} d y

derivative of ln(sqrt(3x+1))

\frac{d}{d x} (ln (3 x + 1))

limit as x approaches 0 of (1-2cos(x)+cos(2x))/(x^2)

x \to 0 lim (\frac{1 - 2 cos ( x ) + cos ( 2 x )}{x ^{2}})

derivative y=-2/5 x-3

d er i v a t i v e y = - \frac{2}{5} x - 3