What is the derivative of ln(ln(15x)) ?

The derivative of ln(ln(15x)) is 1/(xln(15x))

What is the first derivative of ln(ln(15x)) ?

The first derivative of ln(ln(15x)) is 1/(xln(15x))

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\frac{d}{d x} (ln (ln (15 x)))

\frac{1}{x ln ( 15 x )}

Solution steps

\frac{d}{d x} (ln (ln (15 x)))

Apply the chain rule:

\frac{1}{ln ( 15 x )} \frac{d}{d x} (ln (15 x))

= \frac{1}{ln ( 15 x )} \frac{d}{d x} (ln (15 x))

\frac{d}{d x} (ln (15 x)) = \frac{1}{x}

= \frac{1}{ln ( 15 x )} \cdot \frac{1}{x}

Simplify

\frac{1}{ln ( 15 x )} \cdot \frac{1}{x} : \frac{1}{x ln ( 15 x )}

= \frac{1}{x ln ( 15 x )}

t sin (π t)

\int_{3}^{4.5} \frac{x}{8} d x

\int \frac{x ^{3}}{x ^{3} + 1} d x

\int \frac{4 + x}{x ^{2}} d x

\frac{d q}{d t} = 5 - 5 q

What is the derivative of ln(ln(15x)) ?
The derivative of ln(ln(15x)) is 1/(xln(15x))
What is the first derivative of ln(ln(15x)) ?
The first derivative of ln(ln(15x)) is 1/(xln(15x))