What is (\partial)/(\partial x)(ln(ln(x))) ?

The answer to (\partial)/(\partial x)(ln(ln(x))) is 1/(xln(x))

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(\partial)/(\partial x)(ln(ln(x)))

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{\partial}{\partial 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 )}

y^{^{'}} = 8 x + y

y = 6 x, (9, 18)

\frac{\partial}{\partial x} (y arctan (x))

x \to 0 lim (\frac{sin ( x )}{2 x})

\frac{d}{d x} (2 cos (x) + 2 x sin (x))

What is (\partial)/(\partial x)(ln(ln(x))) ?
The answer to (\partial)/(\partial x)(ln(ln(x))) is 1/(xln(x))