What is the first d/(dt)(7t^3) ?

The first d/(dt)(7t^3) is 21t^2

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d/(dt)(7t^3)

\frac{d}{d t} (7 t^{3})

21 t^{2}

Solution steps

\frac{d}{d t} (7 t^{3})

Take the constant out:

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

= 7 \frac{d}{d t} (t^{3})

Apply the Power Rule:

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

= 7 \cdot 3 t^{3 - 1}

Simplify

= 21 t^{2}