de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative y=ln(x+sqrt(x^2-3))

Lösung

ableitung von

y = ln (x + x^{2} - 3)

Lösung

\frac{1}{x ^{2} - 3}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

(dy)/(dx)+5y-20=0

\frac{d y}{d x} + 5 y - 20 = 0

sum from n=1 to infinity of 7

n = 1 \sum \infty 7

fläche x^2,-x+2

a re a x^{2}, - x + 2

integral of 1/(1+3x)

\int \frac{1}{1 + 3 x} d x

limit as x approaches infinity of x^2+4x

x \to \infty lim (x^{2} + 4 x)