What is the derivative of e^{-1x} ?

The derivative of e^{-1x} is -e^{-x}

What is the first derivative of e^{-1x} ?

The first derivative of e^{-1x} is -e^{-x}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

- e^{- x}

Solution steps

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

Simplify

e^{- 1 \cdot x} : e^{- x}

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

Apply the chain rule:

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

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

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

= e^{- x} (- 1)

Simplify

= - e^{- x}

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