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

The answer to (\partial)/(\partial y)((x^2)/(y^2)) is -(2x^2)/(y^3)

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

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

- \frac{2 x ^{2}}{y ^{3}}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

x^{2} (- 2 y^{- 2 - 1}) : - \frac{2 x ^{2}}{y ^{3}}

= - \frac{2 x ^{2}}{y ^{3}}

\frac{d}{d x} (3 x^{5} - 5 x^{3})

\int_{2}^{\infty} - 7 x^{- 2} d x

\frac{d}{d x} ((\frac{x}{3})^{3})

\frac{d}{d x} (\frac{x ^{2} + 2 x - 4}{( x + 1 ) ^{2}})

\int_{1}^{2} \frac{ln ^{2} ( x )}{x ^{3}} d x

What is (\partial)/(\partial y)((x^2)/(y^2)) ?
The answer to (\partial)/(\partial y)((x^2)/(y^2)) is -(2x^2)/(y^3)