What is (\partial)/(\partial x)(xe^{2x}) ?

The answer to (\partial)/(\partial x)(xe^{2x}) is e^{2x}+2e^{2x}x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(xe^{2x})

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{\partial}{\partial x} (x) = 1

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

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

Simplify

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

What is (\partial)/(\partial x)(xe^{2x}) ?
The answer to (\partial)/(\partial x)(xe^{2x}) is e^{2x}+2e^{2x}x