de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative of xln(1/x)

Lösung

\frac{d}{d x} (x ln (\frac{1}{x}))

Lösung

- ln (x) - 1

Schritte zur Lösung

\frac{d}{d x} (x ln (\frac{1}{x}))

Vereinfache

x ln (\frac{1}{x}) : - x ln (x)

= \frac{d}{d x} (- x ln (x))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{d}{d x} (x ln (x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = ln (x)

= - (\frac{d x}{d x} ln (x) + \frac{d}{d x} (ln (x)) x)

\frac{d x}{d x} = 1

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= - (1 \cdot ln (x) + \frac{1}{x} x)

Vereinfache

- (1 \cdot ln (x) + \frac{1}{x} x) : - ln (x) - 1

= - ln (x) - 1

Graph

Beliebte Beispiele

d er i v a t i v e y = 2

(dx)/(dt)=tx^{1/3},x(1)=1

\frac{d x}{d t} = t x^{\frac{1}{3}}, x (1) = 1

integral from 0 to 4 of x/(sqrt(9+x^2))

\int_{0}^{4} \frac{x}{9 + x ^{2}} d x

derivative of 10x^2e^x

\frac{d}{d x} (10 x^{2} e^{x})

derivative (x^3)/3+(x^2)/2+x

d er i v a t i v e \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + x