What is the derivative of 1/(3x^{2/3)} ?

The derivative of 1/(3x^{2/3)} is -2/(9x^{5/3)}

What is the first derivative of 1/(3x^{2/3)} ?

The first derivative of 1/(3x^{2/3)} is -2/(9x^{5/3)}

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derivative of

\frac{1}{3 x ^{\frac{2}{3}}}

- \frac{2}{9 x ^{\frac{5}{3}}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

\frac{1}{3} (- \frac{2}{3} x^{- \frac{2}{3} - 1}) : - \frac{2}{9 x ^{\frac{5}{3}}}

= - \frac{2}{9 x ^{\frac{5}{3}}}

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What is the derivative of 1/(3x^{2/3)} ?
The derivative of 1/(3x^{2/3)} is -2/(9x^{5/3)}
What is the first derivative of 1/(3x^{2/3)} ?
The first derivative of 1/(3x^{2/3)} is -2/(9x^{5/3)}