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Popular >

derivative of xe^{(-x^2})

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

Popular Examples

derivative of ((4x^2+8x+2))/(sqrt(x))derivative of

\frac{( 4 x ^{2} + 8 x + 2 )}{x}

y^'+175x=0,y(2)=0

y^{^{'}} + 175 x = 0, y (2) = 0

(dy)/(dt)=4y+y^3,y(0)=1

\frac{d y}{d t} = 4 y + y^{3}, y (0) = 1

derivative of ln(\sqrt[8]{(x-3/(x+3)}))

laplacetransform te^{-10t}laplace transform

t e^{- 10 t}

Frequently Asked Questions (FAQ)

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