What is the derivative of (x-4ln(x/4)) ?

The derivative of (x-4ln(x/4)) is ln(x/4)+(x-4)/x

What is the first derivative of (x-4ln(x/4)) ?

The first derivative of (x-4ln(x/4)) is ln(x/4)+(x-4)/x

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\frac{d}{d x} ((x - 4) ln (\frac{x}{4}))

ln (\frac{x}{4}) + \frac{x - 4}{x}

Solution steps

\frac{d}{d x} ((x - 4) ln (\frac{x}{4}))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x - 4, g = ln (\frac{x}{4})

= \frac{d}{d x} (x - 4) ln (\frac{x}{4}) + \frac{d}{d x} (ln (\frac{x}{4})) (x - 4)

\frac{d}{d x} (x - 4) = 1

\frac{d}{d x} (ln (\frac{x}{4})) = \frac{1}{x}

= 1 \cdot ln (\frac{x}{4}) + \frac{1}{x} (x - 4)

Simplify

1 \cdot ln (\frac{x}{4}) + \frac{1}{x} (x - 4) : ln (\frac{x}{4}) + \frac{x - 4}{x}

= ln (\frac{x}{4}) + \frac{x - 4}{x}

What is the derivative of (x-4ln(x/4)) ?
The derivative of (x-4ln(x/4)) is ln(x/4)+(x-4)/x
What is the first derivative of (x-4ln(x/4)) ?
The first derivative of (x-4ln(x/4)) is ln(x/4)+(x-4)/x