What is the derivative of f(x)=6\sqrt[3]{x} ?

The derivative of f(x)=6\sqrt[3]{x} is 2/(x^{2/3)}

What is the first derivative of f(x)=6\sqrt[3]{x} ?

The first derivative of f(x)=6\sqrt[3]{x} is 2/(x^{2/3)}

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derivative of

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

Solution steps

Take the constant out:

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

Apply radical rule:

= 6 \frac{d}{d x} (x^{\frac{1}{3}})

Apply the Power Rule:

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

= 6 \cdot \frac{1}{3} x^{\frac{1}{3} - 1}

Simplify

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

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

What is the derivative of f(x)=6\sqrt[3]{x} ?
The derivative of f(x)=6\sqrt[3]{x} is 2/(x^{2/3)}
What is the first derivative of f(x)=6\sqrt[3]{x} ?
The first derivative of f(x)=6\sqrt[3]{x} is 2/(x^{2/3)}