What is the derivative of 1/3 x^{3/2} ?

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

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

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

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derivative of

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

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

Solution steps

\frac{d}{d x} (\frac{1}{3} x^{\frac{3}{2}})

Take the constant out:

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

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

Simplify

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

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

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