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

The derivative of x^2e^{-x} is 2e^{-x}x-e^{-x}x^2

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

f (m) = \frac{1}{lo g _{3} ( m )}

f (x) = 5 x

f (x) = \frac{1}{2 x}

(1, 0)

x e^{- x^{2}}

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