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}}

n = 1 \sum \infty \frac{2}{3 n + 9}

\int_{l n (x)}^{1} sin^{3} (u) d u

y = x^{3} - 12 x^{2} + 32 x, - x^{3} + 12 x^{2} - 32 x

\int e^{\frac{x}{y}} d x

x \to 2 lim (sin (\frac{2}{x - 2}))

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