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

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

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

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

- \frac{1}{y}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= - \frac{1}{y}

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