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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

x e^{- x^{2}}

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}

f (x) = x^{7}

f (x) = 8 - x^{3}

x + y = 3

f (x) = 7 x^{2} + 2 x - 7, at x = - 3

- 3 x + 5 y = 2 x + 3 y

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