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

The d/(dt)(2e^{-t}t-e^{-t}t^2) is e^{-t}t^2-4e^{-t}t+2e^{-t}

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

The first d/(dt)(2e^{-t}t-e^{-t}t^2) is e^{-t}t^2-4e^{-t}t+2e^{-t}

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

e^{- t} t^{2} - 4 e^{- t} t + 2 e^{- t}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

2 (- e^{- t} t + e^{- t}) - (- e^{- t} t^{2} + 2 e^{- t} t) : e^{- t} t^{2} - 4 e^{- t} t + 2 e^{- t}

= e^{- t} t^{2} - 4 e^{- t} t + 2 e^{- t}

What is the d/(dt)(2e^{-t}t-e^{-t}t^2) ?
The d/(dt)(2e^{-t}t-e^{-t}t^2) is e^{-t}t^2-4e^{-t}t+2e^{-t}
What is the first d/(dt)(2e^{-t}t-e^{-t}t^2) ?
The first d/(dt)(2e^{-t}t-e^{-t}t^2) is e^{-t}t^2-4e^{-t}t+2e^{-t}