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

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

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

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

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

- 2 e^{- t^{2}} x t

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

6 e^{- 3 x} \cdot (e^{x} - 1)

e^{4} \cdot e^{5}

e^{2} \cdot e^{- x}

(x \cdot 2 x) \cdot (2 x)

- e^{- 3 t} (e^{- t})

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