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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

2 (- 2 e^{- x^{2}} x^{2} + e^{- x^{2}})

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

= 2 (- 2 e^{- x^{2}} x^{2} + e^{- x^{2}})

\frac{\partial}{\partial y} (e^{2 x + y})

\frac{d}{d θ} (θ cos (θ) sin (θ))

\int \frac{cos ( θ )}{5 + 4 cos ( θ )} d θ

\frac{d}{d y} (3 x^{2} y + e^{y})

\frac{3 x}{4}

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