What is the (ln(ln(x)))^' ?

The (ln(ln(x)))^' is 1/(xln(x))

What is the first (ln(ln(x)))^' ?

The first (ln(ln(x)))^' is 1/(xln(x))

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(ln (ln (x)))^{^{'}}

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

Solution steps

(ln (ln (x)))^{'}

Apply the chain rule:

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

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

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

y = cot^{2} (sin (x))

\frac{\partial}{\partial x} ((\frac{e}{y})^{x})

\int_{0}^{4} (3 t^{4} + 3 t + 2) d t

\frac{\partial}{\partial y} (2 x + 4 y)