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 )}

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

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

x^{3} y^{^{'''}} - 6 y = 0

\int 7 arctan (3 y) d y

\int \frac{6 sin ( 2 x )}{sin ( x )} d 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))