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

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

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d/(dy)(y^{-2})

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

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

Solution steps

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

Apply the Power Rule:

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

= - 2 y^{- 2 - 1}

Simplify

- 2 y^{- 2 - 1} : - \frac{2}{y ^{3}}

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

x - 1

y^{^{'}} = x + 2 y

\int \frac{x ^{2} + 2 x - 1}{x ^{3} - x} d x

\int 6 e^{x + 2 y} d y

y = \frac{4}{- 4 x + 3 + 3 x ^{2}} \frac{d y}{d x}