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

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

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derivative of (x^2/2)

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

x

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

= x

\int 2 x - 3 d x

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\int \frac{x ^{2} - 1}{e ^{\frac{x}{2}}} d x

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\int \frac{x ^{2}}{49 + x ^{2}} d x