What is the derivative of ax^{-2} ?

The derivative of ax^{-2} is -(2a)/(x^3)

What is the first derivative of ax^{-2} ?

The first derivative of ax^{-2} is -(2a)/(x^3)

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

What is the derivative of ax^{-2} ?
The derivative of ax^{-2} is -(2a)/(x^3)
What is the first derivative of ax^{-2} ?
The first derivative of ax^{-2} is -(2a)/(x^3)