What is the derivative of ln|ln(10x)| ?

The derivative of ln|ln(10x)| is 1/(xln(10x))

What is the first derivative of ln|ln(10x)| ?

The first derivative of ln|ln(10x)| is 1/(xln(10x))

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derivative of

ln ∣ ln (10 x) ∣

\frac{1}{x ln ( 10 x )}

Solution steps

\frac{d}{d x} (ln ∣ ln (10 x) ∣)

Apply the chain rule:

\frac{1}{∣ ln ( 10 x ) ∣} \frac{d}{d x} (∣ ln (10 x) ∣)

= \frac{1}{∣ ln ( 10 x ) ∣} \frac{d}{d x} (∣ ln (10 x) ∣)

\frac{d}{d x} (∣ ln (10 x) ∣) = \frac{ln ( 10 x )}{x ∣ ln ( 10 x ) ∣}

= \frac{1}{∣ ln ( 10 x ) ∣} \cdot \frac{ln ( 10 x )}{x ∣ ln ( 10 x ) ∣}

Simplify

\frac{1}{∣ ln ( 10 x ) ∣} \cdot \frac{ln ( 10 x )}{x ∣ ln ( 10 x ) ∣} : \frac{1}{x ln ( 10 x )}

= \frac{1}{x ln ( 10 x )}

What is the derivative of ln|ln(10x)| ?
The derivative of ln|ln(10x)| is 1/(xln(10x))
What is the first derivative of ln|ln(10x)| ?
The first derivative of ln|ln(10x)| is 1/(xln(10x))