en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of-2x(e^{-2x})

Solution

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

Solution

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - 2 \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}

= - 2 (\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}

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

Simplify

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

Popular Examples

derivative of (1-e^{2x}/(1+e^{2x)})

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

integral of (cos(x))/(1-sin^2(x))

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

integral of ((x-2))/1

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

derivative of 9arctan(x+sqrt(1+x^2))

\frac{d}{d x} (9 arctan (x + 1 + x^{2}))

limit as x approaches 4 of (4x)/(x-4)

x \to 4 lim (\frac{4 x}{x - 4})

Frequently Asked Questions (FAQ)

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