en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 1/((1+x^2))

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

limit as x approaches 1-of x

x \to 1 - lim (x)

integral of 2x^9e^{-x^5}

\int 2 x^{9} e^{- x^{5}} d x

integral of 9/(x^2sqrt(x^2+4))

\int \frac{9}{x ^{2} x ^{2} + 4} d x

(\partial)/(\partial x)(x^2+zsin(xyz))

\frac{\partial}{\partial x} (x^{2} + z sin (x yz))

integral of ((1-u^2-u-u^3))/(1+u^2)

\int \frac{( 1 - u ^{2} - u - u ^{3} )}{1 + u ^{2}} d u

Frequently Asked Questions (FAQ)

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