What is the derivative of (e^{x^2}/x) ?

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

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

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

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