What is the derivative of (-2/(x^2)) ?

The derivative of (-2/(x^2)) is 4/(x^3)

What is the first derivative of (-2/(x^2)) ?

The first derivative of (-2/(x^2)) is 4/(x^3)

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

\frac{4}{x ^{3}}

Solution steps

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

Simplify

\frac{- 2}{x ^{2}} : - \frac{2}{x ^{2}}

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

- 2 (- 2 x^{- 2 - 1}) : \frac{4}{x ^{3}}

= \frac{4}{x ^{3}}

What is the derivative of (-2/(x^2)) ?
The derivative of (-2/(x^2)) is 4/(x^3)
What is the first derivative of (-2/(x^2)) ?
The first derivative of (-2/(x^2)) is 4/(x^3)