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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( - 1 ) ( x + y ) - 1 \cdot ( x - y )}{( x + y ) ^{2}} : - \frac{2 x}{( x + y ) ^{2}}

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

\int_{- 1}^{2} (x^{2} - 1) d x

x \to 2 lim (\frac{3}{( x - 2 ) ^{3}})

\int \frac{e ^{2 x}}{( e ^{2 x} + 1 ) ^{3}} d x

\frac{d}{d x} (lo g_{5} (sin^{2} (x)))

\int 441 - x^{2} d x

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