What is the derivative of y=log_{e}(log_{e}(x)) ?

The derivative of y=log_{e}(log_{e}(x)) is 1/(xln(x))

What is the first derivative of y=log_{e}(log_{e}(x)) ?

The first derivative of y=log_{e}(log_{e}(x)) is 1/(xln(x))

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derivative of

y = lo g_{e} (lo g_{e} (x))

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

Solution steps

\frac{d}{d x} (lo g_{e} (lo g_{e} (x)))

Simplify

lo g_{e} (lo g_{e} (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 )} \cdot \frac{1}{x}

Simplify

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

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

h \to 0 lim (\frac{( h + 2 ) ^{3} - 8}{h})

\int \frac{1}{y} d y

\int_{0}^{1} 5 \frac{e ^{\frac{1}{x}}}{x ^{3}} d x

(\frac{8 x + 5}{8 x - 5})^{\frac{1}{2}}

e^{r} + r^{e}

What is the derivative of y=log_{e}(log_{e}(x)) ?
The derivative of y=log_{e}(log_{e}(x)) is 1/(xln(x))
What is the first derivative of y=log_{e}(log_{e}(x)) ?
The first derivative of y=log_{e}(log_{e}(x)) is 1/(xln(x))