What is the derivative of xe^{x^2} ?

The derivative of xe^{x^2} is e^{x^2}+2e^{x^2}x^2

What is the first derivative of xe^{x^2} ?

The first derivative of xe^{x^2} is e^{x^2}+2e^{x^2}x^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative

e^{x^{2}} + 2 e^{x^{2}} x^{2}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{x^{2}}

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

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

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

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

Simplify

1 \cdot e^{x^{2}} + e^{x^{2}} \cdot 2 xx : e^{x^{2}} + 2 e^{x^{2}} x^{2}

= e^{x^{2}} + 2 e^{x^{2}} x^{2}

What is the derivative of xe^{x^2} ?
The derivative of xe^{x^2} is e^{x^2}+2e^{x^2}x^2
What is the first derivative of xe^{x^2} ?
The first derivative of xe^{x^2} is e^{x^2}+2e^{x^2}x^2