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-1|x-1|)

Lösung

\frac{d}{d x} ((x - 1) ∣ x - 1 ∣)

Lösung

\frac{2 ( x - 1 ) ^{2}}{∣ x - 1 ∣}

Schritte zur Lösung

\frac{d}{d x} ((x - 1) ∣ x - 1 ∣)

Wende die Produktregel an:

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

f = x - 1, g = ∣ x - 1 ∣

= \frac{d}{d x} (x - 1) ∣ x - 1 ∣ + \frac{d}{d x} (∣ x - 1 ∣) (x - 1)

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

\frac{d}{d x} (∣ x - 1 ∣) = \frac{x - 1}{∣ x - 1 ∣}

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

Vereinfache

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

= \frac{2 ( x - 1 ) ^{2}}{∣ x - 1 ∣}

Graph

Beliebte Beispiele

integral from 1 to 4 of 6sqrt(t)ln(t)

\int_{1}^{4} 6 t ln (t) d t

integral of sec(2t)tan(2t)

\int sec (2 t) tan (2 t) d t

derivative (8x-6)^2

d er i v a t i v e (8 x - 6)^{2}

integral of ((x^2+5)/((x+2)^2))

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

integral of (x^3)/(x+2)

\int \frac{x ^{3}}{x + 2} d x