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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

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