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

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

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

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

1

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 1 - 0

Simplify

= 1

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