en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

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

Solution

- e^{- x} x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

= - e^{- x} x

Graph

Popular Examples

integral of 9/(x^8)

\int \frac{9}{x ^{8}} d x

integral from 0 to 10 of |x^2-8x+7|

\int_{0}^{10} x^{2} - 8 x + 7 d x

(\partial)/(\partial y)(7x+5y)

\frac{\partial}{\partial y} (7 x + 5 y)

integral of 1/(sqrt(x)+\sqrt[3]{x)}

\int \frac{1}{x + 3 x} d x

(\partial)/(\partial x)(4xcos(5xy))

\frac{\partial}{\partial x} (4 x cos (5 x y))

Frequently Asked Questions (FAQ)

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