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

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

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derivative of (t^2)/2

derivative of

\frac{t ^{2}}{2}

t

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

= t

\int 2 x x^{2} + 5 d x

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x \to - 4 lim (2 x^{7} + 8 x^{4} - 1)

\int (y e^{y^{2}}) d y

x (x - 2)