en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of f(x)=xe^{x^2}

Solution

derivative of

f (x) = x e^{x^{2}}

Solution

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}

Popular Examples

derivative of (5x^2tan(x))/(sec(x))derivative of

\frac{5 x ^{2} tan ( x )}{sec ( x )}

integral of (x^2)/(x-9)

\int \frac{x ^{2}}{x - 9} d x

area 2-x^2,x^2 area

2 - x^{2}, x^{2}

(\partial)/(\partial x)(x^2+2y^2+9xz-12)

\frac{\partial}{\partial x} (x^{2} + 2 y^{2} + 9 x z - 12)

derivative of \sqrt[3]{t}-3e^t derivative of

Frequently Asked Questions (FAQ)

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