What is the derivative of xe^{(-(x^2/8)}) ?

The derivative of xe^{(-(x^2/8)}) is e^{-(x^2)/8}-(e^{-(x^2)/8}x^2)/(4)

What is the first derivative of xe^{(-(x^2/8)}) ?

The first derivative of xe^{(-(x^2/8)}) is e^{-(x^2)/8}-(e^{-(x^2)/8}x^2)/(4)

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\frac{d}{d x} (x e^{(- \frac{x ^{2}}{8})})

e^{- \frac{x ^{2}}{8}} - \frac{e ^{- \frac{x ^{2}}{8}} x ^{2}}{4}

Solution steps

\frac{d}{d x} (x e^{(- \frac{x ^{2}}{8})})

Apply the Product Rule:

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

f = x, g = e^{- \frac{x ^{2}}{8}}

= \frac{d x}{d x} e^{- \frac{x ^{2}}{8}} + \frac{d}{d x} (e^{- \frac{x ^{2}}{8}}) x

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

\frac{d}{d x} (e^{- \frac{x ^{2}}{8}}) = - \frac{e ^{- \frac{x ^{2}}{8}} x}{4}

= 1 \cdot e^{- \frac{x ^{2}}{8}} + (- \frac{e ^{- \frac{x ^{2}}{8}} x}{4}) x

Simplify

1 \cdot e^{- \frac{x ^{2}}{8}} + (- \frac{e ^{- \frac{x ^{2}}{8}} x}{4}) x : e^{- \frac{x ^{2}}{8}} - \frac{e ^{- \frac{x ^{2}}{8}} x ^{2}}{4}

= e^{- \frac{x ^{2}}{8}} - \frac{e ^{- \frac{x ^{2}}{8}} x ^{2}}{4}

f (x) = - \frac{1}{6} (x^{- 6} - x^{12})

x y^{^{'}} + y = x^{\frac{3}{2}} y^{\frac{5}{2}} ln (x)

e^{6 x}

\frac{x + 9}{x}

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

What is the derivative of xe^{(-(x^2/8)}) ?
The derivative of xe^{(-(x^2/8)}) is e^{-(x^2)/8}-(e^{-(x^2)/8}x^2)/(4)
What is the first derivative of xe^{(-(x^2/8)}) ?
The first derivative of xe^{(-(x^2/8)}) is e^{-(x^2)/8}-(e^{-(x^2)/8}x^2)/(4)