What is the d/(dt)((x(t,w))(te^{-wt})) ?

The d/(dt)((x(t,w))(te^{-wt})) is x((,w*1)te^{-wt}+(e^{-wt}-we^{-wt}t)(t,w))

What is the first d/(dt)((x(t,w))(te^{-wt})) ?

The first d/(dt)((x(t,w))(te^{-wt})) is x((,w*1)te^{-wt}+(e^{-wt}-we^{-wt}t)(t,w))

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\frac{d}{d t} ((x (t, w)) (t e^{- wt}))

x ((, w \cdot 1) t e^{- wt} + (e^{- wt} - w e^{- wt} t) (t, w))

Solution steps

\frac{d}{d t} ((x (t, w)) (t e^{- wt}))

Treat

x, w

as constants

Take the constant out:

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

= x \frac{d}{d t} ((t, w) t e^{- wt})

Apply the Product Rule:

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

f = t, w, g = t e^{- wt}

= x (\frac{d}{d t} (t, w) t e^{- wt} + \frac{d}{d t} (t e^{- wt}) (t, w))

\frac{d}{d t} (t, w) = (, w \cdot 1)

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

= x ((, w \cdot 1) t e^{- wt} + (e^{- wt} - w e^{- wt} t) (t, w))

(e^{2 x} - 4) \cdot (e^{2 x} - 4)

e^{- x \cdot 0}

0.4 \cdot 6.4

e^{- 1.762116}

- k e^{- 0}

What is the d/(dt)((x(t,w))(te^{-wt})) ?
The d/(dt)((x(t,w))(te^{-wt})) is x((,w*1)te^{-wt}+(e^{-wt}-we^{-wt}t)(t,w))
What is the first d/(dt)((x(t,w))(te^{-wt})) ?
The first d/(dt)((x(t,w))(te^{-wt})) is x((,w*1)te^{-wt}+(e^{-wt}-we^{-wt}t)(t,w))