What is the derivative of (8x^{1/3}) ?

The derivative of (8x^{1/3}) is 2/(3x^{2/3)}

What is the first derivative of (8x^{1/3}) ?

The first derivative of (8x^{1/3}) is 2/(3x^{2/3)}

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\frac{d}{d x} ((8 x)^{\frac{1}{3}})

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

Solution steps

\frac{d}{d x} ((8 x)^{\frac{1}{3}})

Simplify

(8 x)^{\frac{1}{3}} : 2 x^{\frac{1}{3}}

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

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What is the derivative of (8x^{1/3}) ?
The derivative of (8x^{1/3}) is 2/(3x^{2/3)}
What is the first derivative of (8x^{1/3}) ?
The first derivative of (8x^{1/3}) is 2/(3x^{2/3)}