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

The derivative of (x^3/2) is (3x^2)/2

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

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