What is the derivative of 1/2 ln(2x) ?

The derivative of 1/2 ln(2x) is 1/(2x)

What is the first derivative of 1/2 ln(2x) ?

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

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

\frac{1}{2 x}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{2 x}

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