What is the derivative of 1/3 \sqrt[3]{x} ?

The derivative of 1/3 \sqrt[3]{x} is 1/(9x^{2/3)}

What is the first derivative of 1/3 \sqrt[3]{x} ?

The first derivative of 1/3 \sqrt[3]{x} is 1/(9x^{2/3)}

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\frac{1}{9 x ^{\frac{2}{3}}}

Solution steps

Take the constant out:

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

Apply radical rule:

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

Simplify

\frac{1}{3} \cdot \frac{1}{3} x^{\frac{1}{3} - 1} : \frac{1}{9 x ^{\frac{2}{3}}}

= \frac{1}{9 x ^{\frac{2}{3}}}

\int \frac{x ^{2}}{x ^{6} - 3} d x

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What is the derivative of 1/3 \sqrt[3]{x} ?
The derivative of 1/3 \sqrt[3]{x} is 1/(9x^{2/3)}
What is the first derivative of 1/3 \sqrt[3]{x} ?
The first derivative of 1/3 \sqrt[3]{x} is 1/(9x^{2/3)}