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

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

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

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

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derivative

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

Solution steps

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

Apply radical rule:

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

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