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

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

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

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

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derivative of

ln ∣ ln (x) ∣

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

Solution steps

\frac{d}{d x} (ln ∣ ln (x) ∣)

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d y}{d t} + \frac{1}{20} y = \frac{3}{2}, y (0) = 0

\frac{d}{d t} (t cos (t) - sin (t))

(t^{3})^{^{'}}

\frac{d}{d x} ((\frac{x ^{3} - 1}{x ^{3} + 1})^{8})

f (x) = 1 + sin (x), at x = π

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