What is the first d/(dy)(y^{-1}) ?

The first d/(dy)(y^{-1}) is -1/(y^2)

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d/(dy)(y^{-1})

\frac{d}{d y} (y^{- 1})

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

Solution steps

\frac{d}{d y} (y^{- 1})

Apply the Power Rule:

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

= - 1 \cdot y^{- 1 - 1}

Simplify

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

= - \frac{1}{y ^{2}}

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

x \to 0 lim (x \cdot arctan (\frac{1}{x}))

\int (2 x^{3} + 3 x + 1)^{4} (6 x^{2} + 3) d x

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

(ln (1 - x^{2}))^{^{'}}