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

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

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

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 1 - x, g = (1 + x^{2})^{- 1}

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

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

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

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

Simplify

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

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

\int \frac{9 + x + x}{x} d x

n = 1 \sum \infty arctan (19 n)

\int - 4 x^{2} sin (π x) d x

f (x) = 5 x + 1, at x = 3

\frac{\partial}{\partial x} (x - 3 y^{2} + 4 x^{2} y^{3})

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