What is the d/(dt)(0.5t^2e^{-0.6t}) ?

The d/(dt)(0.5t^2e^{-0.6t}) is 0.5(2e^{-0.6t}t-0.6e^{-0.6t}t^2)

What is the first d/(dt)(0.5t^2e^{-0.6t}) ?

The first d/(dt)(0.5t^2e^{-0.6t}) is 0.5(2e^{-0.6t}t-0.6e^{-0.6t}t^2)

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\frac{d}{d t} (0.5 t^{2} e^{- 0.6 t})

0.5 (2 e^{- 0.6 t} t - 0.6 e^{- 0.6 t} t^{2})

Solution steps

\frac{d}{d t} (0.5 t^{2} e^{- 0.6 t})

Take the constant out:

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

= 0.5 \frac{d}{d t} (t^{2} e^{- 0.6 t})

Apply the Product Rule:

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

f = t^{2}, g = e^{- 0.6 t}

= 0.5 (\frac{d}{d t} (t^{2}) e^{- 0.6 t} + \frac{d}{d t} (e^{- 0.6 t}) t^{2})

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

\frac{d}{d t} (e^{- 0.6 t}) = - 0.6 e^{- 0.6 t}

= 0.5 (2 t e^{- 0.6 t} + (- 0.6 e^{- 0.6 t}) t^{2})

Simplify

= 0.5 (2 e^{- 0.6 t} t - 0.6 e^{- 0.6 t} t^{2})

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What is the d/(dt)(0.5t^2e^{-0.6t}) ?
The d/(dt)(0.5t^2e^{-0.6t}) is 0.5(2e^{-0.6t}t-0.6e^{-0.6t}t^2)
What is the first d/(dt)(0.5t^2e^{-0.6t}) ?
The first d/(dt)(0.5t^2e^{-0.6t}) is 0.5(2e^{-0.6t}t-0.6e^{-0.6t}t^2)