What is the derivative of 3/2 x^{2/3} ?

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

What is the first derivative of 3/2 x^{2/3} ?

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

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