What is the d/(dt)((x)(xe^{-x})) ?

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

What is the first d/(dt)((x)(xe^{-x})) ?

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

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

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

Solution steps

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

Simplify

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

(6 n^{2} p^{4}) (n^{3} p^{2})

(5 z^{3}) (9 z^{3})

(6 x^{3} y^{2}) (7 y^{5})

3.5 x 1 0^{- 1}

(1.26 \cdot 1 0^{- 3}) 2

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