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

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

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

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

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

\frac{1}{2 x}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{2 x}

\frac{d}{d x} (x^{\frac{2}{3}} (x - 4))

\frac{d}{d x} ((2 x - 8)^{5})

f (t) = t^{2} e^{3 t}

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

\frac{d}{d x} (x^{3} + x^{2} + x + 1)

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