en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = 2 x + 1, g = e^{- x}

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

\frac{d}{d x} (2 x + 1) = 2

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

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

Simplify

2 e^{- x} + (- e^{- x}) (2 x + 1) : - 2 e^{- x} x + e^{- x}

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

Graph

Popular Examples

sum from n=0 to infinity of 2/(n^2+2n)

n = 0 \sum \infty \frac{2}{n ^{2} + 2 n}

integral of (x^2+3)/(x^3+2x)

\int \frac{x ^{2} + 3}{x ^{3} + 2 x} d x

derivative of ln(3x^2-y^3-3)

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

derivative of 3^{x^2cot(2x})

\frac{d}{d x} (3^{x^{2} c o t (2 x)})

derivative of 8/(\sqrt[3]{x})

\frac{d}{d x} (\frac{8}{3 x})

Frequently Asked Questions (FAQ)

What is the derivative of (2x+1e^{-x}) ?
The derivative of (2x+1e^{-x}) is -2e^{-x}x+e^{-x}
What is the first derivative of (2x+1e^{-x}) ?
The first derivative of (2x+1e^{-x}) is -2e^{-x}x+e^{-x}