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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Expand

2 (2 x + y) - 2 (2 x - y) : 4 y

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

\frac{d y}{d x} + \frac{y}{x} = 8 x^{7} y^{2}

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

(1.5) (- 1.7)

\int 4 x y^{3} d x

f (x) = 2 x + 3

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