What is the d/(dt)(t^2e^{-t}) ?

The d/(dt)(t^2e^{-t}) is 2e^{-t}t-e^{-t}t^2

What is the first d/(dt)(t^2e^{-t}) ?

The first d/(dt)(t^2e^{-t}) is 2e^{-t}t-e^{-t}t^2

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

2 e^{- t} t - e^{- t} t^{2}

Solution steps

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

Apply the Product Rule:

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

f = t^{2}, g = e^{- t}

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

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

\frac{d}{d t} (e^{- t}) = - e^{- t}

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

Simplify

= 2 e^{- t} t - e^{- t} t^{2}

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\int \frac{x - 1}{x ^{2} + 4} d x

What is the d/(dt)(t^2e^{-t}) ?
The d/(dt)(t^2e^{-t}) is 2e^{-t}t-e^{-t}t^2
What is the first d/(dt)(t^2e^{-t}) ?
The first d/(dt)(t^2e^{-t}) is 2e^{-t}t-e^{-t}t^2