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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

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