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

The answer to (\partial}{\partial x}(\frac{x-y)/x) is y/(x^2)

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

\frac{1 \cdot x - 1 \cdot ( x - y )}{x ^{2}} : \frac{y}{x ^{2}}

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

\frac{d}{d x} (ln (\frac{x}{4}) (x - 4))

\int \frac{sin ( x )}{cot ( x )} d x

\frac{s}{s ^{2} - 16}

y^{^{'}} = x^{2} - y - 2, y (0) = 1

\int \frac{x ^{2}}{( x ^{2} - 2 x + 2 ) ^{2}} d x

What is (\partial}{\partial x}(\frac{x-y)/x) ?
The answer to (\partial}{\partial x}(\frac{x-y)/x) is y/(x^2)