en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

((x^2-1)/(x^2+1))^'

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

(x^{2} - 1)^{'} = 2 x

(x^{2} + 1)^{'} = 2 x

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

Expand

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

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

Popular Examples

integral of 2/(x^3-2x^2+9x-18)

\int \frac{2}{x ^{3} - 2 x ^{2} + 9 x - 18} d x

derivative of 3e^{-x}+e^{4x}derivative of

3 e^{- x} + e^{4 x}

derivative of (4x+5/(4x-5))

\frac{d}{d x} (\frac{4 x + 5}{4 x - 5})

integral of ((e^x-e^{-x})/(e^x+e^{-x)})

\int (\frac{e ^{x} - e ^{- x}}{e ^{x} + e ^{- x}}) d x

integral of (6x)/((4-3x^2)^4)

\int \frac{6 x}{( 4 - 3 x ^{2} ) ^{4}} d x

Frequently Asked Questions (FAQ)

What is the ((x^2-1)/(x^2+1))^' ?
The ((x^2-1)/(x^2+1))^' is (4x)/((x^2+1)^2)
What is the first ((x^2-1)/(x^2+1))^' ?
The first ((x^2-1)/(x^2+1))^' is (4x)/((x^2+1)^2)