What is the (e^{-3x^2})^' ?

The (e^{-3x^2})^' is -6e^{-3x^2}x

What is the first (e^{-3x^2})^' ?

The first (e^{-3x^2})^' is -6e^{-3x^2}x

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(e^{- 3 x^{2}})^{^{'}}

- 6 e^{- 3 x^{2}} x

Solution steps

(e^{- 3 x^{2}})^{'}

Apply the chain rule:

e^{- 3 x^{2}} (- 3 x^{2})^{'}

= e^{- 3 x^{2}} (- 3 x^{2})^{'}

(- 3 x^{2})^{'} = - 6 x

= e^{- 3 x^{2}} (- 6 x)

Simplify

= - 6 e^{- 3 x^{2}} x

e^{- (\frac{5}{10})^{2}}

60 (2)^{- 0.02 \cdot 561}

\frac{( e ^{x^{2}} )}{( e ^{x} )}

(2 x 1 0^{3}) (1.5 x 1 0^{2})

70 \cdot 3^{- 0.03 \cdot 387}