What is the derivative of ln(ln(2x^3)) ?

The derivative of ln(ln(2x^3)) is 3/(xln(2x^3))

What is the first derivative of ln(ln(2x^3)) ?

The first derivative of ln(ln(2x^3)) is 3/(xln(2x^3))

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\frac{d}{d x} (ln (ln (2 x^{3})))

\frac{3}{x ln ( 2 x ^{3} )}

Solution steps

\frac{d}{d x} (ln (ln (2 x^{3})))

Apply the chain rule:

\frac{1}{ln ( 2 x ^{3} )} \frac{d}{d x} (ln (2 x^{3}))

= \frac{1}{ln ( 2 x ^{3} )} \frac{d}{d x} (ln (2 x^{3}))

\frac{d}{d x} (ln (2 x^{3})) = \frac{3}{x}

= \frac{1}{ln ( 2 x ^{3} )} \cdot \frac{3}{x}

Simplify

\frac{1}{ln ( 2 x ^{3} )} \cdot \frac{3}{x} : \frac{3}{x ln ( 2 x ^{3} )}

= \frac{3}{x ln ( 2 x ^{3} )}

What is the derivative of ln(ln(2x^3)) ?
The derivative of ln(ln(2x^3)) is 3/(xln(2x^3))
What is the first derivative of ln(ln(2x^3)) ?
The first derivative of ln(ln(2x^3)) is 3/(xln(2x^3))