What is (\partial}{\partial y}(\frac{(x-y))/x) ?

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

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

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

- \frac{1}{x}

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Sum/Difference Rule:

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

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

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

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

= \frac{1}{x} (0 - 1)

Simplify

= - \frac{1}{x}

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