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

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

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

The first derivative of x^2*e^{-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 >

\frac{d}{d x} (x^{2} \cdot 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}

\int_{0}^{1} x 3^{x} d x

25 - 5 x ln (0.04 x) - x

x \to 0 + lim (- 4 csc^{2} (4 x))

\int \frac{x - 4}{x ^{2} - x - 6} d x

2 x d y + y d x = 0

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