What is the derivative of (1/2 x)^3 ?

The derivative of (1/2 x)^3 is (3x^2)/8

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

The first derivative of (1/2 x)^3 is (3x^2)/8

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derivative of

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

\frac{3 x ^{2}}{8}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

3 (\frac{1}{2} x)^{2} \frac{1}{2} : \frac{3 x ^{2}}{8}

= \frac{3 x ^{2}}{8}

What is the derivative of (1/2 x)^3 ?
The derivative of (1/2 x)^3 is (3x^2)/8
What is the first derivative of (1/2 x)^3 ?
The first derivative of (1/2 x)^3 is (3x^2)/8