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

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

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

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

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derivative of

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

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