en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ln|ln(3x|)

Solution

\frac{d}{d x} (ln ∣ ln (3 x) ∣)

Solution

\frac{1}{x ln ( 3 x )}

Solution steps

\frac{d}{d x} (ln ∣ ln (3 x) ∣)

Apply the chain rule:

\frac{1}{∣ ln ( 3 x ) ∣} \frac{d}{d x} (∣ ln (3 x) ∣)

= \frac{1}{∣ ln ( 3 x ) ∣} \frac{d}{d x} (∣ ln (3 x) ∣)

\frac{d}{d x} (∣ ln (3 x) ∣) = \frac{ln ( 3 x )}{x ∣ ln ( 3 x ) ∣}

= \frac{1}{∣ ln ( 3 x ) ∣} \cdot \frac{ln ( 3 x )}{x ∣ ln ( 3 x ) ∣}

Simplify

\frac{1}{∣ ln ( 3 x ) ∣} \cdot \frac{ln ( 3 x )}{x ∣ ln ( 3 x ) ∣} : \frac{1}{x ln ( 3 x )}

= \frac{1}{x ln ( 3 x )}

Graph

Popular Examples

derivative of e^{2x-4}

\frac{d}{d x} (e^{2 x - 4})

derivative of sqrt((3x^{2/3)-2})

\frac{d}{d x} ((3 x)^{\frac{2}{3}} - 2)

derivative of f(x)=(2x)/(x^2+4)derivative of

f (x) = \frac{2 x}{x ^{2} + 4}

integral of-9x^2sec(3x^3+1)tan(3x^3+1)

\int - 9 x^{2} sec (3 x^{3} + 1) tan (3 x^{3} + 1) d x

integral of inx

\int in x d x

Frequently Asked Questions (FAQ)

What is the derivative of ln|ln(3x|) ?
The derivative of ln|ln(3x|) is 1/(xln(3x))
What is the first derivative of ln|ln(3x|) ?
The first derivative of ln|ln(3x|) is 1/(xln(3x))