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

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

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

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

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

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

Solution steps

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

Apply the Power Rule:

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

= \frac{1}{3} x^{\frac{1}{3} - 1}

Simplify

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

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

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