What is the derivative of 6x^{1/3} ?

The derivative of 6x^{1/3} is 2/(x^{2/3)}

What is the first derivative of 6x^{1/3} ?

The first derivative of 6x^{1/3} is 2/(x^{2/3)}

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

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

Solution steps

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

Take the constant out:

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

= 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 6x^{1/3} ?
The derivative of 6x^{1/3} is 2/(x^{2/3)}
What is the first derivative of 6x^{1/3} ?
The first derivative of 6x^{1/3} is 2/(x^{2/3)}