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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

x \to - 2 - lim (\frac{x + 5}{x + 4})

\frac{d}{d x} ((x^{2} - 9)^{\frac{2}{3}})

\int (3 x^{2} + 2 x - 3) d x

n = 1 \sum \infty \frac{9}{( n + 1 ) !}

f (x) = 8 x^{2}, at x = 10

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