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Popular Calculus >

derivative of (3x^3/2)

Solution

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

Solution

\frac{9 x ^{2}}{2}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

\frac{3}{2} \cdot 3 x^{3 - 1} : \frac{9 x ^{2}}{2}

= \frac{9 x ^{2}}{2}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (3x^3/2) ?
The derivative of (3x^3/2) is (9x^2)/2
What is the first derivative of (3x^3/2) ?
The first derivative of (3x^3/2) is (9x^2)/2