What is (\partial)/(\partial y)(x^2+2xy+y^2) ?

The answer to (\partial)/(\partial y)(x^2+2xy+y^2) is 2x+2y

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial y)(x^2+2xy+y^2)

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

2 x + 2 y

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial y} (x^{2}) = 0

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

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

= 0 + 2 x + 2 y

Simplify

= 2 x + 2 y

What is (\partial)/(\partial y)(x^2+2xy+y^2) ?
The answer to (\partial)/(\partial y)(x^2+2xy+y^2) is 2x+2y