What is the derivative of e^{1/t} ?

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

What is the first derivative of e^{1/t} ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

e^{\frac{1}{t}}

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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