What is the derivative of 2ln(sqrt(3x-1)) ?

The derivative of 2ln(sqrt(3x-1)) is 3/(3x-1)

What is the first derivative of 2ln(sqrt(3x-1)) ?

The first derivative of 2ln(sqrt(3x-1)) is 3/(3x-1)

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derivative of

2 ln (3 x - 1)

\frac{3}{3 x - 1}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

\frac{1}{3 x - 1} \frac{d}{d x} (3 x - 1)

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

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

= 2 \cdot \frac{1}{3 x - 1} \cdot \frac{3}{2 3 x - 1}

Simplify

2 \cdot \frac{1}{3 x - 1} \cdot \frac{3}{2 3 x - 1} : \frac{3}{3 x - 1}

= \frac{3}{3 x - 1}

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What is the derivative of 2ln(sqrt(3x-1)) ?
The derivative of 2ln(sqrt(3x-1)) is 3/(3x-1)
What is the first derivative of 2ln(sqrt(3x-1)) ?
The first derivative of 2ln(sqrt(3x-1)) is 3/(3x-1)