What is the derivative of ln(ln(5x)) ?

The derivative of ln(ln(5x)) is 1/(xln(5x))

What is the first derivative of ln(ln(5x)) ?

The first derivative of ln(ln(5x)) is 1/(xln(5x))

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derivative of

ln (ln (5 x))

\frac{1}{x ln ( 5 x )}

Solution steps

\frac{d}{d x} (ln (ln (5 x)))

Apply the chain rule:

\frac{1}{ln ( 5 x )} \frac{d}{d x} (ln (5 x))

= \frac{1}{ln ( 5 x )} \frac{d}{d x} (ln (5 x))

\frac{d}{d x} (ln (5 x)) = \frac{1}{x}

= \frac{1}{ln ( 5 x )} \cdot \frac{1}{x}

Simplify

\frac{1}{ln ( 5 x )} \cdot \frac{1}{x} : \frac{1}{x ln ( 5 x )}

= \frac{1}{x ln ( 5 x )}

x \to \infty lim ((1 + \frac{3}{x})^{\frac{x}{4}})

h (x) = ln (x + x^{2} - 7)

\frac{- 2 s + 1}{s ^{2} + 2 s - 8}

x \to 0 lim (\frac{x + 4}{x})

\int \frac{3}{( x + 5 ) ^{2} + 4} d x

What is the derivative of ln(ln(5x)) ?
The derivative of ln(ln(5x)) is 1/(xln(5x))
What is the first derivative of ln(ln(5x)) ?
The first derivative of ln(ln(5x)) is 1/(xln(5x))