What is the first d/(dt)((t^4)/4) ?

The first d/(dt)((t^4)/4) is t^3

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d/(dt)((t^4)/4)

\frac{d}{d t} (\frac{t ^{4}}{4})

t^{3}

Solution steps

\frac{d}{d t} (\frac{t ^{4}}{4})

Take the constant out:

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

= \frac{1}{4} \frac{d}{d t} (t^{4})

Apply the Power Rule:

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

= \frac{1}{4} \cdot 4 t^{4 - 1}

Simplify

\frac{1}{4} \cdot 4 t^{4 - 1} : t^{3}

= t^{3}

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