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))

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derivative of

ln (ln (3 x))

\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{1}{x}

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

Simplify

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

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

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))