What is the derivative of \sqrt[3]{u} ?

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

What is the first derivative of \sqrt[3]{u} ?

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

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derivative of

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

Solution steps

Apply radical rule:

= \frac{d}{d u} (u^{\frac{1}{3}})

Apply the Power Rule:

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

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

Simplify

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

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

f (x) = x^{3}, at x = - 3

x \to - 2 lim (x - 2)

\frac{d}{d x} (2 + x)

\int e^{- \frac{1}{2}} d x

\frac{d y}{d x}, y^{5} = x^{6}

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