What is the derivative of ln(ln(9x)) ?

The derivative of ln(ln(9x)) is 1/(xln(9x))

What is the first derivative of ln(ln(9x)) ?

The first derivative of ln(ln(9x)) is 1/(xln(9x))

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

\frac{1}{x ln ( 9 x )}

Solution steps

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

Apply the chain rule:

\frac{1}{ln ( 9 x )} \frac{d}{d x} (ln (9 x))

= \frac{1}{ln ( 9 x )} \frac{d}{d x} (ln (9 x))

\frac{d}{d x} (ln (9 x)) = \frac{1}{x}

= \frac{1}{ln ( 9 x )} \cdot \frac{1}{x}

Simplify

\frac{1}{ln ( 9 x )} \cdot \frac{1}{x} : \frac{1}{x ln ( 9 x )}

= \frac{1}{x ln ( 9 x )}

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\frac{d}{d x} (- \frac{5 e ^{\frac{5}{x}}}{x ^{2}})

\frac{\partial}{\partial x} (30 - (x^{2} + y^{2}))

\int sin^{5} (11 x) d x

\int ([sin (x)]^{2} x + [cos (x)]^{2} x) d x

What is the derivative of ln(ln(9x)) ?
The derivative of ln(ln(9x)) is 1/(xln(9x))
What is the first derivative of ln(ln(9x)) ?
The first derivative of ln(ln(9x)) is 1/(xln(9x))