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

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

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

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

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

Solution steps

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

Simplify

\frac{- x}{y} : - \frac{x}{y}

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

Treat

x

as a constant

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

Simplify

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

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

\int \frac{y + 2}{y} d y

n = 1 \sum \infty \frac{( - 1 ) ^{n - 1}}{n n}

\frac{d ^{2}}{d x ^{2}} (\frac{x}{x - 4})

sin (x) tan (2 x) + cos (x), 0

n = 2 \sum \infty (- 1)^{n} \frac{n + 1}{2 n - 3}

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