What is the derivative of f(x)=ln(ln(x)) ?

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

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

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

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derivative of

f (x) = ln (ln (x))

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

Solution steps

\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 )} \cdot \frac{1}{x}

Simplify

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

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

\int e^{- 0.02 t} (e^{- 0.13 t} + 4) d t

n = 0 \sum \infty n 5

\int_{0}^{x} \frac{1}{0.2 x + 10} d x

1 - x^{2}

\int \frac{3 x + 1}{4 - x ^{2}} d x

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