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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

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