What is the d/(dy)(-x/(y^2)) ?

The d/(dy)(-x/(y^2)) is (2x)/(y^3)

What is the first d/(dy)(-x/(y^2)) ?

The first d/(dy)(-x/(y^2)) is (2x)/(y^3)

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

= - x \frac{d}{d 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}}

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