What is the d/(dt)(t^2(3-t)^3) ?

The d/(dt)(t^2(3-t)^3) is 2t(3-t)^3-3t^2(3-t)^2

What is the first d/(dt)(t^2(3-t)^3) ?

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

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

2 t (3 - t)^{3} - 3 t^{2} (3 - t)^{2}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = t^{2}, g = (3 - t)^{3}

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

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

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

= 2 t (3 - t)^{3} + (- 3 (3 - t)^{2}) t^{2}

Simplify

= 2 t (3 - t)^{3} - 3 t^{2} (3 - t)^{2}

What is the d/(dt)(t^2(3-t)^3) ?
The d/(dt)(t^2(3-t)^3) is 2t(3-t)^3-3t^2(3-t)^2
What is the first d/(dt)(t^2(3-t)^3) ?
The first d/(dt)(t^2(3-t)^3) is 2t(3-t)^3-3t^2(3-t)^2