What is the (1/2 \sqrt[3]{x})^' ?

The (1/2 \sqrt[3]{x})^' is 1/(6x^{2/3)}

What is the first (1/2 \sqrt[3]{x})^' ?

The first (1/2 \sqrt[3]{x})^' is 1/(6x^{2/3)}

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

\frac{1}{6 x ^{\frac{2}{3}}}

Solution steps

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

Take the constant out:

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

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

Apply radical rule:

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

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

Apply the Power Rule:

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

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

Simplify

\frac{1}{2} \cdot \frac{1}{3} x^{\frac{1}{3} - 1} : \frac{1}{6 x ^{\frac{2}{3}}}

= \frac{1}{6 x ^{\frac{2}{3}}}

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What is the (1/2 \sqrt[3]{x})^' ?
The (1/2 \sqrt[3]{x})^' is 1/(6x^{2/3)}
What is the first (1/2 \sqrt[3]{x})^' ?
The first (1/2 \sqrt[3]{x})^' is 1/(6x^{2/3)}