What is the derivative of e^{(1/x}) ?

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

What is the first derivative of e^{(1/x}) ?

The first derivative of e^{(1/x}) is -(e^{1/x})/(x^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

- \frac{e ^{\frac{1}{x}}}{x ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{e ^{\frac{1}{x}}}{x ^{2}}

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