en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y=(1-x)/(1+x)

Solution

derivative of

y = \frac{1 - x}{1 + x}

Solution

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

Solution steps

\frac{d}{d x} (\frac{1 - x}{1 + x})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

limit as x approaches infinity of x^2e^{-x}

x \to \infty lim (x^{2} e^{- x})

integral of 1/2 sin((2pix)/5)

\int \frac{1}{2} sin (\frac{2 π x}{5}) d x

(dy)/(dt)=3y-e^{(3t)}+6t^2-2

\frac{d y}{d t} = 3 y - e^{(3 t)} + 6 t^{2} - 2

derivative of (5x+8^2)

\frac{d}{d x} ((5 x + 8)^{2})

y^{''}+25y=5csc^2(5t)

y^{^{''}} + 25 y = 5 csc^{2} (5 t)

Frequently Asked Questions (FAQ)

What is the derivative of y=(1-x)/(1+x) ?
The derivative of y=(1-x)/(1+x) is -2/((1+x)^2)
What is the first derivative of y=(1-x)/(1+x) ?
The first derivative of y=(1-x)/(1+x) is -2/((1+x)^2)