What is the derivative of 1/8 x-ln(2x) ?

The derivative of 1/8 x-ln(2x) is 1/8-1/x

What is the first derivative of 1/8 x-ln(2x) ?

The first derivative of 1/8 x-ln(2x) is 1/8-1/x

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\frac{d}{d x} (\frac{1}{8} x - ln (2 x))

\frac{1}{8} - \frac{1}{x}

Solution steps

\frac{d}{d x} (\frac{1}{8} x - ln (2 x))

Simplify

\frac{1}{8} x - ln (2 x) : \frac{x}{8} - ln (2 x)

= \frac{d}{d x} (\frac{x}{8} - ln (2 x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{x}{8}) - \frac{d}{d x} (ln (2 x))

\frac{d}{d x} (\frac{x}{8}) = \frac{1}{8}

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

= \frac{1}{8} - \frac{1}{x}

What is the derivative of 1/8 x-ln(2x) ?
The derivative of 1/8 x-ln(2x) is 1/8-1/x
What is the first derivative of 1/8 x-ln(2x) ?
The first derivative of 1/8 x-ln(2x) is 1/8-1/x