What is the derivative of (1-x^2/((1+x^2)^2)) ?

The derivative of (1-x^2/((1+x^2)^2)) is -(2x(-x^2+3))/((x^2+1)^3)

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

The first derivative of (1-x^2/((1+x^2)^2)) is -(2x(-x^2+3))/((x^2+1)^3)

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

- \frac{2 x ( - x ^{2} + 3 )}{( x ^{2} + 1 ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} ((1 + x^{2})^{2}) = 4 x (1 + x^{2})

= \frac{( - 2 x ) ( 1 + x ^{2} ) ^{2} - 4 x ( 1 + x ^{2} ) ( 1 - x ^{2} )}{( ( 1 + x ^{2} ) ^{2} ) ^{2}}

Simplify

\frac{( - 2 x ) ( 1 + x ^{2} ) ^{2} - 4 x ( 1 + x ^{2} ) ( 1 - x ^{2} )}{( ( 1 + x ^{2} ) ^{2} ) ^{2}} : - \frac{2 x ( - x ^{2} + 3 )}{( x ^{2} + 1 ) ^{3}}

= - \frac{2 x ( - x ^{2} + 3 )}{( x ^{2} + 1 ) ^{3}}

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 2 y = e^{2 x}

\int x \cdot 5^{x} d x

\frac{e ^{- s}}{s - 1}

- 4 t^{2} + 15 t + 8

\int (5 x^{2} + 1)^{2} (10 x) d x

What is the derivative of (1-x^2/((1+x^2)^2)) ?
The derivative of (1-x^2/((1+x^2)^2)) is -(2x(-x^2+3))/((x^2+1)^3)
What is the first derivative of (1-x^2/((1+x^2)^2)) ?
The first derivative of (1-x^2/((1+x^2)^2)) is -(2x(-x^2+3))/((x^2+1)^3)