What is (\partial)/(\partial x)(4x^2y-2x+2y^3) ?

The answer to (\partial)/(\partial x)(4x^2y-2x+2y^3) is 8xy-2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(4x^2y-2x+2y^3)

\frac{\partial}{\partial x} (4 x^{2} y - 2 x + 2 y^{3})

8 x y - 2

Solution steps

\frac{\partial}{\partial x} (4 x^{2} y - 2 x + 2 y^{3})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (4 x^{2} y) - \frac{\partial}{\partial x} (2 x) + \frac{\partial}{\partial x} (2 y^{3})

\frac{\partial}{\partial x} (4 x^{2} y) = 8 y x

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

\frac{\partial}{\partial x} (2 y^{3}) = 0

= 8 y x - 2 + 0

Simplify

= 8 x y - 2

What is (\partial)/(\partial x)(4x^2y-2x+2y^3) ?
The answer to (\partial)/(\partial x)(4x^2y-2x+2y^3) is 8xy-2