What is the first derivative of 0.5x^2 ?

The first derivative of 0.5x^2 is x

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derivative of 0.5x^2

\frac{d}{d x} (0.5 x^{2})

x

Solution steps

\frac{d}{d x} (0.5 x^{2})

Take the constant out:

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

= 0.5 \frac{d}{d x} (x^{2})

Apply the Power Rule:

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

= 0.5 \cdot 2 x^{2 - 1}

Simplify

= x