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

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

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

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

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

A (2 e^{- t} t - e^{- t} t^{2})

Solution steps

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

Take the constant out:

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

= A \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}

= A (\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}

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

Simplify

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

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