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

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

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

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

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derivative of

y = 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 )}

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

x \to 4 - lim (x^{2} + \frac{2}{x + 4})

x \to \infty lim (3^{- x})

(1, - 1), (5, - 7)

\frac{d}{d x} (arctan (x) + arctan (\frac{1}{x}))

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