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

The derivative of (x-3/x+ln(x/3)) is 3/(x^2)+1/x

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

The first derivative of (x-3/x+ln(x/3)) is 3/(x^2)+1/x

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

\frac{3}{x ^{2}} + \frac{1}{x}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= \frac{3}{x ^{2}} + \frac{1}{x}

What is the derivative of (x-3/x+ln(x/3)) ?
The derivative of (x-3/x+ln(x/3)) is 3/(x^2)+1/x
What is the first derivative of (x-3/x+ln(x/3)) ?
The first derivative of (x-3/x+ln(x/3)) is 3/(x^2)+1/x