What is the derivative of-1/2 e^{-x^2} ?

The derivative of-1/2 e^{-x^2} is e^{-x^2}x

What is the first derivative of-1/2 e^{-x^2} ?

The first derivative of-1/2 e^{-x^2} is e^{-x^2}x

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\frac{d}{d x} (- \frac{1}{2} e^{- x^{2}})

e^{- x^{2}} x

Solution steps

\frac{d}{d x} (- \frac{1}{2} e^{- x^{2}})

Take the constant out:

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

= - \frac{1}{2} \frac{d}{d x} (e^{- x^{2}})

Apply the chain rule:

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

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

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

= - \frac{1}{2} e^{- x^{2}} (- 2 x)

Simplify

- \frac{1}{2} e^{- x^{2}} (- 2 x) : e^{- x^{2}} x

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

What is the derivative of-1/2 e^{-x^2} ?
The derivative of-1/2 e^{-x^2} is e^{-x^2}x
What is the first derivative of-1/2 e^{-x^2} ?
The first derivative of-1/2 e^{-x^2} is e^{-x^2}x