What is the derivative of ln|ln(5x)| ?

The derivative of ln|ln(5x)| is 1/(xln(5x))

What is the first derivative of ln|ln(5x)| ?

The first derivative of ln|ln(5x)| is 1/(xln(5x))

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derivative of

ln ∣ ln (5 x) ∣

\frac{1}{x ln ( 5 x )}

Solution steps

\frac{d}{d x} (ln ∣ ln (5 x) ∣)

Apply the chain rule:

\frac{1}{∣ ln ( 5 x ) ∣} \frac{d}{d x} (∣ ln (5 x) ∣)

= \frac{1}{∣ ln ( 5 x ) ∣} \frac{d}{d x} (∣ ln (5 x) ∣)

\frac{d}{d x} (∣ ln (5 x) ∣) = \frac{ln ( 5 x )}{x ∣ ln ( 5 x ) ∣}

= \frac{1}{∣ ln ( 5 x ) ∣} \cdot \frac{ln ( 5 x )}{x ∣ ln ( 5 x ) ∣}

Simplify

\frac{1}{∣ ln ( 5 x ) ∣} \cdot \frac{ln ( 5 x )}{x ∣ ln ( 5 x ) ∣} : \frac{1}{x ln ( 5 x )}

= \frac{1}{x ln ( 5 x )}

\int \frac{4}{x ln ( 9 x )} d x

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

\int cos (2 k x) d x

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

\int \frac{x}{x ^{2} - x + 1} d x

What is the derivative of ln|ln(5x)| ?
The derivative of ln|ln(5x)| is 1/(xln(5x))
What is the first derivative of ln|ln(5x)| ?
The first derivative of ln|ln(5x)| is 1/(xln(5x))