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

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

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

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

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

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

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

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