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 1/2 x^2

derivative of

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

x

Solution steps

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

\frac{\partial}{\partial x} (x^{3} + y^{3} - 27 x - 12 y)

\int 3 x^{3} e^{x} d x

\int t^{3} ln (t^{2}) d t

(- 2 cos (2 x) - sin (3 x) - 3)^{2}

y^{^{''}} + y = 0, y (0) = 0, y^{^{'}} (0) = 0