What is the derivative of ln(ln(6x)) ?

The derivative of ln(ln(6x)) is 1/(xln(6x))

What is the first derivative of ln(ln(6x)) ?

The first derivative of ln(ln(6x)) is 1/(xln(6x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (ln (ln (6 x)))

\frac{1}{x ln ( 6 x )}

Solution steps

\frac{d}{d x} (ln (ln (6 x)))

Apply the chain rule:

\frac{1}{ln ( 6 x )} \frac{d}{d x} (ln (6 x))

= \frac{1}{ln ( 6 x )} \frac{d}{d x} (ln (6 x))

\frac{d}{d x} (ln (6 x)) = \frac{1}{x}

= \frac{1}{ln ( 6 x )} \cdot \frac{1}{x}

Simplify

\frac{1}{ln ( 6 x )} \cdot \frac{1}{x} : \frac{1}{x ln ( 6 x )}

= \frac{1}{x ln ( 6 x )}

What is the derivative of ln(ln(6x)) ?
The derivative of ln(ln(6x)) is 1/(xln(6x))
What is the first derivative of ln(ln(6x)) ?
The first derivative of ln(ln(6x)) is 1/(xln(6x))