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

The answer to (\partial)/(\partial y)((2x)/(y^2)) is -(4x)/(y^3)

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

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

- \frac{4 x}{y ^{3}}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

2 x (- 2 y^{- 2 - 1}) : - \frac{4 x}{y ^{3}}

= - \frac{4 x}{y ^{3}}

What is (\partial)/(\partial y)((2x)/(y^2)) ?
The answer to (\partial)/(\partial y)((2x)/(y^2)) is -(4x)/(y^3)