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

The derivative of 2xe^{-x}-x^2e^{-x} is 2e^{-x}-4e^{-x}x+e^{-x}x^2

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

The first derivative of 2xe^{-x}-x^2e^{-x} is 2e^{-x}-4e^{-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} (2 x e^{- x} - x^{2} e^{- x})

2 e^{- x} - 4 e^{- x} x + e^{- x} x^{2}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

2 (e^{- x} - e^{- x} x) - (2 e^{- x} x - e^{- x} x^{2}) : 2 e^{- x} - 4 e^{- x} x + e^{- x} x^{2}

= 2 e^{- x} - 4 e^{- x} x + e^{- x} x^{2}

\frac{d y}{d x} = (\frac{4 x}{( 1 + x ^{2} ) ^{\frac{1}{3}}})

\frac{d}{d x} (3 x^{2} sin (x) tan (x))

ln (x^{2} + 6)

12 x

\int \frac{1}{( x - 2 ) ( x ^{2} + 1 )} d x

What is the derivative of 2xe^{-x}-x^2e^{-x} ?
The derivative of 2xe^{-x}-x^2e^{-x} is 2e^{-x}-4e^{-x}x+e^{-x}x^2
What is the first derivative of 2xe^{-x}-x^2e^{-x} ?
The first derivative of 2xe^{-x}-x^2e^{-x} is 2e^{-x}-4e^{-x}x+e^{-x}x^2