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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

Find the Derivative - d/dx 2e^(-2x)

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

- x \frac{d}{d x} (2 e^{- 2 x}) - 4 e^{- 2 x} x - 2 e^{- 2 x} + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply Integration By Parts

: \frac{d}{d x} (2 e^{- 2 x}) x - \int 8 e^{- 2 x} x d x

= - (\frac{d}{d x} (2 e^{- 2 x}) x - \int 8 e^{- 2 x} x d x)

\int 8 e^{- 2 x} x d x = 2 (- 2 e^{- 2 x} x - e^{- 2 x})

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

Simplify

- (\frac{d}{d x} (2 e^{- 2 x}) x - 2 (- 2 e^{- 2 x} x - e^{- 2 x})) : - x \frac{d}{d x} (2 e^{- 2 x}) - 4 e^{- 2 x} x - 2 e^{- 2 x}

= - x \frac{d}{d x} (2 e^{- 2 x}) - 4 e^{- 2 x} x - 2 e^{- 2 x}

Add a constant to the solution

= - x \frac{d}{d x} (2 e^{- 2 x}) - 4 e^{- 2 x} x - 2 e^{- 2 x} + C

- \frac{d}{d} y y^{2}

\frac{- 1}{( e ^{x} )}

- \frac{d}{d x} y = 4 x

- \frac{d}{d x} y = 2 x^{2}

- \frac{d}{d x} (cot (2 x))

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