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}

\int 3 x e^{3 z} + 5 d z

\frac{( s - 1 ) ^{3}}{s ^{4}}

x \to 0 lim (\frac{x ^{2} - 6 x + 9}{x ^{2}})

\frac{d}{d x} (x^{3} - 12 x^{2} + 36 x)

9 (5 x^{4} ln (7 x) + x^{4})

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