What is (\partial)/(\partial x)(xy+ln(x/y)) ?

The answer to (\partial)/(\partial x)(xy+ln(x/y)) is y+1/x

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(\partial)/(\partial x)(xy+ln(x/y))

\frac{\partial}{\partial x} (x y + ln (\frac{x}{y}))

y + \frac{1}{x}

Solution steps

\frac{\partial}{\partial x} (x y + ln (\frac{x}{y}))

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x y) + \frac{\partial}{\partial x} (ln (\frac{x}{y}))

\frac{\partial}{\partial x} (x y) = y

\frac{\partial}{\partial x} (ln (\frac{x}{y})) = \frac{1}{x}

= y + \frac{1}{x}

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What is (\partial)/(\partial x)(xy+ln(x/y)) ?
The answer to (\partial)/(\partial x)(xy+ln(x/y)) is y+1/x