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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

x \to 0 lim (\frac{7}{1 + x})

\frac{d}{d x} (3 x^{2} - x^{4})

\int (\frac{2 x ^{3} + 10 x ^{2} + 8 x - 12}{4 x}) d x

\int \frac{x}{x ^{2} + 9} d x

y^{^{'''}} + 2 y^{^{''}} - 10 y^{^{'}} - 20 y = 0

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