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)=((5x-2))/((x^2+1))

Lösung

ableitung von

f (x) = \frac{( 5 x - 2 )}{( x ^{2} + 1 )}

Lösung

\frac{- 5 x ^{2} + 4 x + 5}{( x ^{2} + 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{5 x - 2}{x ^{2} + 1})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 5 x - 2 ) ( x ^{2} + 1 ) - \frac{d}{d x} ( x ^{2} + 1 ) ( 5 x - 2 )}{( x ^{2} + 1 ) ^{2}}

\frac{d}{d x} (5 x - 2) = 5

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

= \frac{5 ( x ^{2} + 1 ) - 2 x ( 5 x - 2 )}{( x ^{2} + 1 ) ^{2}}

Multipliziere aus

5 (x^{2} + 1) - 2 x (5 x - 2) : - 5 x^{2} + 4 x + 5

= \frac{- 5 x ^{2} + 4 x + 5}{( x ^{2} + 1 ) ^{2}}

Graph

Beliebte Beispiele

integral from 0 to pi/8 of sec^2(2x)

\int_{0}^{\frac{π}{8}} sec^{2} (2 x) d x

integral from 0 to pi/6 of 1

\int_{0}^{\frac{π}{6}} 1

limit as x approaches 0-of x^{sin(x)}

x \to 0 - lim (x^{s i n (x)})

derivative y=(1+sqrt(x))^3

d er i v a t i v e y = (1 + x)^{3}

derivative (x^2-100)/(x+10)

d er i v a t i v e \frac{x ^{2} - 100}{x + 10}