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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

= - \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

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

Simplify

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

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