What is the derivative of ln(ln(8x)) ?

The derivative of ln(ln(8x)) is 1/(xln(8x))

What is the first derivative of ln(ln(8x)) ?

The first derivative of ln(ln(8x)) is 1/(xln(8x))

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derivative of

ln (ln (8 x))

\frac{1}{x ln ( 8 x )}

Solution steps

\frac{d}{d x} (ln (ln (8 x)))

Apply the chain rule:

\frac{1}{ln ( 8 x )} \frac{d}{d x} (ln (8 x))

= \frac{1}{ln ( 8 x )} \frac{d}{d x} (ln (8 x))

\frac{d}{d x} (ln (8 x)) = \frac{1}{x}

= \frac{1}{ln ( 8 x )} \cdot \frac{1}{x}

Simplify

\frac{1}{ln ( 8 x )} \cdot \frac{1}{x} : \frac{1}{x ln ( 8 x )}

= \frac{1}{x ln ( 8 x )}

\frac{- x ^{3}}{y ^{3}}

y = 4 x, y = 2 x^{2}

14 x^{3} + 7 x^{2} + 11 x - 29

\frac{d y}{d x} = \frac{4 x sec ( \frac{y}{x} ) + y}{x}

\int \frac{1}{2} e^{5 x + 6} d x

What is the derivative of ln(ln(8x)) ?
The derivative of ln(ln(8x)) is 1/(xln(8x))
What is the first derivative of ln(ln(8x)) ?
The first derivative of ln(ln(8x)) is 1/(xln(8x))