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

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

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

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

y + \frac{1}{y}

Solution steps

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

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

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

= y + \frac{1}{y}

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