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

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

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

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

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العربية

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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