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

The derivative of y=xe^{-2x} is e^{-2x}-2e^{-2x}x

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = x e^{- 2 x}

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

\frac{1}{2} sin^{2} (x)

x \to - 1 lim ((1 + \frac{1}{x})^{x})

\int x^{3} - 2 x d x

x \to - 16 lim (14)

\frac{\partial}{\partial x} (2 cos^{2} (x))

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