What is the derivative of (x-3*ln(x/3)) ?

The derivative of (x-3*ln(x/3)) is ln(x/3)+(x-3)/x

What is the first derivative of (x-3*ln(x/3)) ?

The first derivative of (x-3*ln(x/3)) is ln(x/3)+(x-3)/x

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\frac{d}{d x} ((x - 3) \cdot ln (\frac{x}{3}))

ln (\frac{x}{3}) + \frac{x - 3}{x}

Solution steps

\frac{d}{d x} ((x - 3) ln (\frac{x}{3}))

Apply the Product Rule:

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

f = x - 3, g = ln (\frac{x}{3})

= \frac{d}{d x} (x - 3) ln (\frac{x}{3}) + \frac{d}{d x} (ln (\frac{x}{3})) (x - 3)

\frac{d}{d x} (x - 3) = 1

\frac{d}{d x} (ln (\frac{x}{3})) = \frac{1}{x}

= 1 \cdot ln (\frac{x}{3}) + \frac{1}{x} (x - 3)

Simplify

1 \cdot ln (\frac{x}{3}) + \frac{1}{x} (x - 3) : ln (\frac{x}{3}) + \frac{x - 3}{x}

= ln (\frac{x}{3}) + \frac{x - 3}{x}

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

\frac{d}{d x} (\frac{3 - 4 x}{x ^{2} + 1})

x \to 1 - lim (2^{\frac{1}{x - 1}})

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

θ sin (θ)

What is the derivative of (x-3*ln(x/3)) ?
The derivative of (x-3*ln(x/3)) is ln(x/3)+(x-3)/x
What is the first derivative of (x-3*ln(x/3)) ?
The first derivative of (x-3*ln(x/3)) is ln(x/3)+(x-3)/x