What is the derivative of ln(ln(6x)) ?

The derivative of ln(ln(6x)) is 1/(xln(6x))

What is the first derivative of ln(ln(6x)) ?

The first derivative of ln(ln(6x)) is 1/(xln(6x))

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\frac{d}{d x} (ln (ln (6 x)))

\frac{1}{x ln ( 6 x )}

Solution steps

\frac{d}{d x} (ln (ln (6 x)))

Apply the chain rule:

\frac{1}{ln ( 6 x )} \frac{d}{d x} (ln (6 x))

= \frac{1}{ln ( 6 x )} \frac{d}{d x} (ln (6 x))

\frac{d}{d x} (ln (6 x)) = \frac{1}{x}

= \frac{1}{ln ( 6 x )} \cdot \frac{1}{x}

Simplify

\frac{1}{ln ( 6 x )} \cdot \frac{1}{x} : \frac{1}{x ln ( 6 x )}

= \frac{1}{x ln ( 6 x )}

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\frac{d}{d x} (x^{2} ln (\frac{1}{x}))

\frac{\partial}{\partial x} (9 cos (x y) x)

x^{^{''}} + k^{2} x = 0

What is the derivative of ln(ln(6x)) ?
The derivative of ln(ln(6x)) is 1/(xln(6x))
What is the first derivative of ln(ln(6x)) ?
The first derivative of ln(ln(6x)) is 1/(xln(6x))