de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative of (x^2-9/(x^2+9))

Lösung

\frac{d}{d x} (\frac{x ^{2} - 9}{x ^{2} + 9})

Lösung

\frac{36 x}{( x ^{2} + 9 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} - 9}{x ^{2} + 9})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} - 9 ) ( x ^{2} + 9 ) - \frac{d}{d x} ( x ^{2} + 9 ) ( x ^{2} - 9 )}{( x ^{2} + 9 ) ^{2}}

\frac{d}{d x} (x^{2} - 9) = 2 x

\frac{d}{d x} (x^{2} + 9) = 2 x

= \frac{2 x ( x ^{2} + 9 ) - 2 x ( x ^{2} - 9 )}{( x ^{2} + 9 ) ^{2}}

Multipliziere aus

2 x (x^{2} + 9) - 2 x (x^{2} - 9) : 36 x

= \frac{36 x}{( x ^{2} + 9 ) ^{2}}

Graph

Beliebte Beispiele

x^{''}+x^'+2x=0

x^{^{''}} + x^{^{'}} + 2 x = 0

(dy)/(dx)=2y(3-y)

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

derivative y=5arctan(x-sqrt(1+x^2))

d er i v a t i v e y = 5 arctan (x - 1 + x^{2})

integral of 1/(y^2-3y)

\int \frac{1}{y ^{2} - 3 y} d y

fläche y=-x+4,y=(x^2)/3

a re a y = - x + 4, y = \frac{x ^{2}}{3}