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

The answer to (\partial)/(\partial x)(2ye^{x^2+y^2}) is 4e^{x^2+y^2}yx

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(2ye^{x^2+y^2})

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

= 4 e^{x^{2} + y^{2}} y x

What is (\partial)/(\partial x)(2ye^{x^2+y^2}) ?
The answer to (\partial)/(\partial x)(2ye^{x^2+y^2}) is 4e^{x^2+y^2}yx