What is the derivative of y=ln(log_{e}(2x)) ?

The derivative of y=ln(log_{e}(2x)) is 1/(xln(2x))

What is the first derivative of y=ln(log_{e}(2x)) ?

The first derivative of y=ln(log_{e}(2x)) is 1/(xln(2x))

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derivative of

y = ln (lo g_{e} (2 x))

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

Solution steps

\frac{d}{d x} (ln (lo g_{e} (2 x)))

Simplify

ln (lo g_{e} (2 x)) : ln (ln (2 x))

= \frac{d}{d x} (ln (ln (2 x)))

Apply the chain rule:

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

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

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

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

Simplify

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

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

n = 1 \sum \infty (x - 2)^{n}

\int cos (x) 1 + sin^{2} (x) d x

\frac{d}{d x} (\frac{4 x ^{3}}{3} - x)

y = (x - 2) (x + 1) (x + 2)

\int a^{- 3 x} d x

What is the derivative of y=ln(log_{e}(2x)) ?
The derivative of y=ln(log_{e}(2x)) is 1/(xln(2x))
What is the first derivative of y=ln(log_{e}(2x)) ?
The first derivative of y=ln(log_{e}(2x)) is 1/(xln(2x))