What is the derivative of-1/2 x^2 ?

The derivative of-1/2 x^2 is -x

What is the first derivative of-1/2 x^2 ?

The first derivative of-1/2 x^2 is -x

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derivative of

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

- x

Solution steps

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

Simplify

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

= \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

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f (x) = \frac{1}{7 ( 1 + x ^{2} )}, g (x) = \frac{1}{14 x ^{2}}

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