What is (\partial)/(\partial x)(1/2 x^2) ?

The answer to (\partial)/(\partial x)(1/2 x^2) is x

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(\partial)/(\partial x)(1/2 x^2)

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

x

Solution steps

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

Take the constant out:

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

= \frac{1}{2} \frac{\partial}{\partial 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

What is (\partial)/(\partial x)(1/2 x^2) ?
The answer to (\partial)/(\partial x)(1/2 x^2) is x