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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derivative of

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}}}

(\frac{x ^{5} + 1}{x}) (x^{5} + 1)

4 x - 5

(e^{x + 1})^{\frac{1}{2}}

\frac{d}{d t} (100 - 10 t + 6 t^{2})

y = x^{7} + 3 x^{5} + 1

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)}