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

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

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

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

\frac{y - 2 x}{y}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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

g (t) = 3 + t^{5} + sin (π t)

x^{3} (x - 6)^{2}

\int x ln (x^{3}) d x

\frac{\partial}{\partial x} (\frac{2 x - y}{x + 4 y})

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