de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative h(w)=(w^2-1)/(w^2+1)

Lösung

ableitung von

h (w) = \frac{w ^{2} - 1}{w ^{2} + 1}

Lösung

\frac{4 w}{( w ^{2} + 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d w} (\frac{w ^{2} - 1}{w ^{2} + 1})

Wende die Quotientenregel an:

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

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

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

\frac{d}{d w} (w^{2} + 1) = 2 w

= \frac{2 w ( w ^{2} + 1 ) - 2 w ( w ^{2} - 1 )}{( w ^{2} + 1 ) ^{2}}

Multipliziere aus

2 w (w^{2} + 1) - 2 w (w^{2} - 1) : 4 w

= \frac{4 w}{( w ^{2} + 1 ) ^{2}}

Graph

Beliebte Beispiele

derivative of (x^3/(12))

\frac{d}{d x} (\frac{x ^{3}}{12})

derivative 1/2 (9t^2+t)^{-3}

d er i v a t i v e \frac{1}{2} (9 t^{2} + t)^{- 3}

integral from 0 to 1 of x^2+sqrt(x)

\int_{0}^{1} x^{2} + x d x

y^{''}+y=0,y(0)=0

y^{^{''}} + y = 0, y (0) = 0

d/(d{r)}(sqrt(4-{r)^2})

\frac{d}{d r} (4 - r^{2})