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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

f^{^{'}} (x) = 2 sec (x) + 3 tan (x) - tan (\frac{π}{3})

y^{^{''}} + (\frac{1}{x}) y^{^{'}} = 0

\int 4 e^{2} d x

y^{^{'}} = \frac{- ( x y + 1 )}{x y + 1}

y^{^{'}} = (x - 3) (y + 1)^{\frac{2}{3}}

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