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

The derivative of 2/(3x^{1/3}) is -2/(9x^{4/3)}

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

The first derivative of 2/(3x^{1/3}) is -2/(9x^{4/3)}

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

- \frac{2}{9 x ^{\frac{4}{3}}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

\frac{2}{3} (- \frac{1}{3} x^{- \frac{1}{3} - 1}) : - \frac{2}{9 x ^{\frac{4}{3}}}

= - \frac{2}{9 x ^{\frac{4}{3}}}

\int_{3}^{5} \frac{x}{x ^{2} - 3} d x

(6 x^{2} - 10 x) e^{x}

y^{^{'}} = \frac{y - x y}{x ^{2}}

\int 10 sin^{6} (x) cos^{3} (x) d x

e^{5 x}

What is the derivative of 2/(3x^{1/3}) ?
The derivative of 2/(3x^{1/3}) is -2/(9x^{4/3)}
What is the first derivative of 2/(3x^{1/3}) ?
The first derivative of 2/(3x^{1/3}) is -2/(9x^{4/3)}