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

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

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

The first derivative of (e^x/x) is (e^xx-e^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} (\frac{e ^{x}}{x})

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d x}{d x} = 1

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

Simplify

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

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