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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the Power Rule:

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

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

Simplify

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

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

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