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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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