What is the derivative of ln(ln(1/x)) ?

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

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

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

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

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

Solution steps

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

Simplify

ln (ln (\frac{1}{x})) : ln (- ln (x))

= \frac{d}{d x} (ln (- ln (x)))

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{- ln ( x )} (- \frac{1}{x}) : \frac{1}{x ln ( x )}

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

y^{^{'}} + y = 2

\int \frac{1}{15 + 4 t - t ^{2}} d t

\frac{1}{1 - x}, 22

\frac{s}{s ^{2} + 2}

f (x) = 4 x - 32 x, at x = 4

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