What is (\partial)/(\partial x)(x^2y-3xy+xy^2) ?

The answer to (\partial)/(\partial x)(x^2y-3xy+xy^2) is 2yx-3y+y^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(x^2y-3xy+xy^2)

\frac{\partial}{\partial x} (x^{2} y - 3 x y + x y^{2})

2 y x - 3 y + y^{2}

Solution steps

\frac{\partial}{\partial x} (x^{2} y - 3 x y + x y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{2} y) - \frac{\partial}{\partial x} (3 x y) + \frac{\partial}{\partial x} (x y^{2})

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

\frac{\partial}{\partial x} (3 x y) = 3 y

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

= 2 y x - 3 y + y^{2}

What is (\partial)/(\partial x)(x^2y-3xy+xy^2) ?
The answer to (\partial)/(\partial x)(x^2y-3xy+xy^2) is 2yx-3y+y^2