What is the derivative of ln|ln(7x)| ?

The derivative of ln|ln(7x)| is 1/(xln(7x))

What is the first derivative of ln|ln(7x)| ?

The first derivative of ln|ln(7x)| is 1/(xln(7x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

ln ∣ ln (7 x) ∣

\frac{1}{x ln ( 7 x )}

Solution steps

\frac{d}{d x} (ln ∣ ln (7 x) ∣)

Apply the chain rule:

\frac{1}{∣ ln ( 7 x ) ∣} \frac{d}{d x} (∣ ln (7 x) ∣)

= \frac{1}{∣ ln ( 7 x ) ∣} \frac{d}{d x} (∣ ln (7 x) ∣)

\frac{d}{d x} (∣ ln (7 x) ∣) = \frac{ln ( 7 x )}{x ∣ ln ( 7 x ) ∣}

= \frac{1}{∣ ln ( 7 x ) ∣} \cdot \frac{ln ( 7 x )}{x ∣ ln ( 7 x ) ∣}

Simplify

\frac{1}{∣ ln ( 7 x ) ∣} \cdot \frac{ln ( 7 x )}{x ∣ ln ( 7 x ) ∣} : \frac{1}{x ln ( 7 x )}

= \frac{1}{x ln ( 7 x )}

What is the derivative of ln|ln(7x)| ?
The derivative of ln|ln(7x)| is 1/(xln(7x))
What is the first derivative of ln|ln(7x)| ?
The first derivative of ln|ln(7x)| is 1/(xln(7x))