What is (\partial)/(\partial x)(ln|x|) ?

The answer to (\partial)/(\partial x)(ln|x|) is 1/x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(ln|x|)

\frac{\partial}{\partial x} (ln ∣ x ∣)

\frac{1}{x}

Solution steps

\frac{\partial}{\partial x} (ln ∣ x ∣)

Apply the chain rule:

\frac{1}{∣ x ∣} \frac{\partial}{\partial x} (∣ x ∣)

= \frac{1}{∣ x ∣} \frac{\partial}{\partial x} (∣ x ∣)

\frac{\partial}{\partial x} (∣ x ∣) = \frac{x}{∣ x ∣}

= \frac{1}{∣ x ∣} \cdot \frac{x}{∣ x ∣}

Simplify

\frac{1}{∣ x ∣} \cdot \frac{x}{∣ x ∣} : \frac{1}{x}

= \frac{1}{x}

x \to 0 lim (3 x ln (x))

x \to 3 lim (8 x^{2} + 9)

\frac{x - 3}{x - 3}

x^{3}, 3 x - 2

What is (\partial)/(\partial x)(ln|x|) ?
The answer to (\partial)/(\partial x)(ln|x|) is 1/x