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

The derivative of 1/(ln(ln(ln(x)))) is -1/(xln^2(ln(ln(x)))ln(ln(x))ln(x))

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

The first derivative of 1/(ln(ln(ln(x)))) is -1/(xln^2(ln(ln(x)))ln(ln(x))ln(x))

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

- \frac{1}{x ln ^{2} ( ln ( ln ( x ) ) ) ln ( ln ( x ) ) ln ( x )}

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

- \frac{1}{( ln ( ln ( ln ( x ) ) ) ) ^{2}} \frac{d}{d x} (ln (ln (ln (x))))

= - \frac{1}{( ln ( ln ( ln ( x ) ) ) ) ^{2}} \frac{d}{d x} (ln (ln (ln (x))))

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

= - \frac{1}{( ln ( ln ( ln ( x ) ) ) ) ^{2}} \cdot \frac{1}{x ln ( ln ( x ) ) ln ( x )}

Simplify

- \frac{1}{ln ^{2} ( ln ( ln ( x ) ) )} \cdot \frac{1}{x ln ( ln ( x ) ) ln ( x )} : - \frac{1}{x ln ^{2} ( ln ( ln ( x ) ) ) ln ( ln ( x ) ) ln ( x )}

= - \frac{1}{x ln ^{2} ( ln ( ln ( x ) ) ) ln ( ln ( x ) ) ln ( x )}

f (x) = (2 x^{- 2} + 3)^{- 3}

tan (2 t)

\frac{d}{d x} (e^{x} (sin (x)))

3 sin (t) cos (t)

\frac{3}{s ^{3}}

What is the derivative of 1/(ln(ln(ln(x)))) ?
The derivative of 1/(ln(ln(ln(x)))) is -1/(xln^2(ln(ln(x)))ln(ln(x))ln(x))
What is the first derivative of 1/(ln(ln(ln(x)))) ?
The first derivative of 1/(ln(ln(ln(x)))) is -1/(xln^2(ln(ln(x)))ln(ln(x))ln(x))