What is the first derivative of 2t^3 ?

The first derivative of 2t^3 is 6t^2

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derivative of 2t^3

derivative of

2 t^{3}

6 t^{2}

Solution steps

\frac{d}{d t} (2 t^{3})

Take the constant out:

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

= 2 \frac{d}{d t} (t^{3})

Apply the Power Rule:

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

= 2 \cdot 3 t^{3 - 1}

Simplify

= 6 t^{2}