What is the derivative of arccos(|x+1|) ?

The derivative of arccos(|x+1|) is -(x+1)/(|x+1|sqrt(-x^2-2x))

What is the first derivative of arccos(|x+1|) ?

The first derivative of arccos(|x+1|) is -(x+1)/(|x+1|sqrt(-x^2-2x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

arccos (∣ x + 1 ∣)

- \frac{x + 1}{∣ x + 1 ∣ - x ^{2} - 2 x}

Solution steps

\frac{d}{d x} (arccos (∣ x + 1 ∣))

Apply the chain rule:

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

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

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

= - \frac{1}{1 - ∣ x + 1 ∣ ^{2}} \cdot \frac{x + 1}{∣ x + 1 ∣}

Simplify

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

= - \frac{x + 1}{∣ x + 1 ∣ - x ^{2} - 2 x}

What is the derivative of arccos(|x+1|) ?
The derivative of arccos(|x+1|) is -(x+1)/(|x+1|sqrt(-x^2-2x))
What is the first derivative of arccos(|x+1|) ?
The first derivative of arccos(|x+1|) is -(x+1)/(|x+1|sqrt(-x^2-2x))