What is the derivative of (x-y/(x+y)) ?

The derivative of (x-y/(x+y)) is (-2x\frac{dy)/(dx)+2y}{(x+y)^2}

What is the first derivative of (x-y/(x+y)) ?

The first derivative of (x-y/(x+y)) is (-2x\frac{dy)/(dx)+2y}{(x+y)^2}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

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

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

\int (x^{2} - 3 x + 5) d x

f (x) = x^{2} + x, at x = 1, at x = 3

\frac{d}{d o} (ln (o))

x \to - 6 lim (\frac{- 5 x}{x + 6})

\frac{d y}{d x} = \frac{18 ( y - 1 )}{( 3 x - 3 ) ^{2}}, y (3) = 3

What is the derivative of (x-y/(x+y)) ?
The derivative of (x-y/(x+y)) is (-2x\frac{dy)/(dx)+2y}{(x+y)^2}
What is the first derivative of (x-y/(x+y)) ?
The first derivative of (x-y/(x+y)) is (-2x\frac{dy)/(dx)+2y}{(x+y)^2}