What is the derivative of ln(1/(sqrt(6x))) ?

The derivative of ln(1/(sqrt(6x))) is -1/(2x)

What is the first derivative of ln(1/(sqrt(6x))) ?

The first derivative of ln(1/(sqrt(6x))) is -1/(2x)

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\frac{d}{d x} (ln (\frac{1}{6 x}))

- \frac{1}{2 x}

Solution steps

\frac{d}{d x} (ln (\frac{1}{6 x}))

Simplify

ln (\frac{1}{6 x}) : - ln (6 x)

= \frac{d}{d x} (- ln (6 x))

Take the constant out:

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

= - \frac{d}{d x} (ln (6 x))

Apply the chain rule:

\frac{1}{6 x} \frac{d}{d x} (6 x)

= \frac{1}{6 x} \frac{d}{d x} (6 x)

\frac{d}{d x} (6 x) = \frac{3}{2 x}

= - \frac{1}{6 x} \cdot \frac{3}{2 x}

Simplify

- \frac{1}{6 x} \cdot \frac{3}{2 x} : - \frac{1}{2 x}

= - \frac{1}{2 x}

What is the derivative of ln(1/(sqrt(6x))) ?
The derivative of ln(1/(sqrt(6x))) is -1/(2x)
What is the first derivative of ln(1/(sqrt(6x))) ?
The first derivative of ln(1/(sqrt(6x))) is -1/(2x)