What is the first (-x^{-2})^' ?

The first (-x^{-2})^' is 2/(x^3)

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(-x^{-2})^'

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

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

Solution steps

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

Take the constant out:

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

= - (x^{- 2})^{^{'}}

Apply the Power Rule:

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

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

Simplify

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

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

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