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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = e^{- \frac{x ^{2}}{2}}, g = x

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

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

\frac{d x}{d x} = 1

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

Simplify

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

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

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