What is the d/(dt)(4/3 pit^3) ?

The d/(dt)(4/3 pit^3) is 4pit^2

What is the first d/(dt)(4/3 pit^3) ?

The first d/(dt)(4/3 pit^3) is 4pit^2

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\frac{d}{d t} (\frac{4}{3} π t^{3})

4 π t^{2}

Solution steps

\frac{d}{d t} (\frac{4}{3} π t^{3})

Take the constant out:

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

= \frac{4}{3} π \frac{d}{d t} (t^{3})

Apply the Power Rule:

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

= \frac{4}{3} π 3 t^{3 - 1}

Simplify

\frac{4}{3} π 3 t^{3 - 1} : 4 π t^{2}

= 4 π t^{2}