What is the derivative of 5xe^{x^2} ?

The derivative of 5xe^{x^2} is 5(e^{x^2}+2e^{x^2}x^2)

What is the first derivative of 5xe^{x^2} ?

The first derivative of 5xe^{x^2} is 5(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

Popular >

\frac{d}{d x} (5 x e^{x^{2}})

5 (e^{x^{2}} + 2 e^{x^{2}} x^{2})

Solution steps

\frac{d}{d x} (5 x e^{x^{2}})

Take the constant out:

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

= 5 \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}}

= 5 (\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

= 5 (1 \cdot e^{x^{2}} + e^{x^{2}} \cdot 2 xx)

Simplify

5 (1 \cdot e^{x^{2}} + e^{x^{2}} \cdot 2 xx) : 5 (e^{x^{2}} + 2 e^{x^{2}} x^{2})

= 5 (e^{x^{2}} + 2 e^{x^{2}} x^{2})

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

\frac{d}{d x} (\frac{4}{x} - \frac{1}{6 x ^{3}} + \frac{8}{x ^{5}})

\int x^{3} 121 - x^{2} d x

6 x e^{x}

10 (x^{3} - x)^{4}

What is the derivative of 5xe^{x^2} ?
The derivative of 5xe^{x^2} is 5(e^{x^2}+2e^{x^2}x^2)
What is the first derivative of 5xe^{x^2} ?
The first derivative of 5xe^{x^2} is 5(e^{x^2}+2e^{x^2}x^2)