de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative of ln(1+1/(x^2))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

steigung f(1)= 8/x-xsqrt(x)

integral of 8sin^2(x)

derivative of 3*e^{3x}

integral of x^2-5x+9

laplacetransform 1+te^t