What is (\partial)/(\partial x)(xy-1/x-1/y) ?

The answer to (\partial)/(\partial x)(xy-1/x-1/y) is 1/(x^2)+y

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(\partial)/(\partial x)(xy-1/x-1/y)

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

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

Solution steps

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

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

\frac{\partial}{\partial x} (\frac{1}{x}) = - \frac{1}{x ^{2}}

\frac{\partial}{\partial x} (\frac{1}{y}) = 0

= y - (- \frac{1}{x ^{2}}) - 0

Simplify

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

f (x) = \frac{1}{x - 2}

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What is (\partial)/(\partial x)(xy-1/x-1/y) ?
The answer to (\partial)/(\partial x)(xy-1/x-1/y) is 1/(x^2)+y