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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\frac{d}{d x} (\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}}}

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

\frac{\partial}{\partial x} (e^{x} + cos (y))

f (x) = \frac{3 x - 7}{5 x - 2}

\frac{d}{d x} (\frac{2}{3} x^{2} - 5 x + \frac{3}{x} + 7)

y = 20 - x, y = x, y = 1

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)}