What is (\partial)/(\partial x)((-x^2)/(y^2)) ?

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

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(\partial)/(\partial x)((-x^2)/(y^2))

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

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

Solution steps

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

Simplify

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

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

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