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

The answer to (\partial)/(\partial x)((x+y)(2x+y)^2) is 12x^2+16xy+5y^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

12 x^{2} + 16 x y + 5 y^{2}

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

f = x + y, g = (2 x + y)^{2}

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

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

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

= 1 \cdot (2 x + y)^{2} + 4 (2 x + y) (x + y)

Simplify

1 \cdot (2 x + y)^{2} + 4 (2 x + y) (x + y) : 12 x^{2} + 16 x y + 5 y^{2}

= 12 x^{2} + 16 x y + 5 y^{2}

y d x + 3 x d y = 0

\int \frac{1}{x x ^{2} - 49} d x

x \to + 0 lim (\frac{e ^{- 1 x} - 1}{x})

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

y = x^{0.95}

What is (\partial)/(\partial x)((x+y)(2x+y)^2) ?
The answer to (\partial)/(\partial x)((x+y)(2x+y)^2) is 12x^2+16xy+5y^2