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}}

Simplify

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

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

Graph

Popular Examples

sum from n=0 to infinity of 1/(n^{1.01)}

n = 0 \sum \infty \frac{1}{n ^{1.01}}

limit as x approaches 5 of x^2-3x

x \to 5 lim (x^{2} - 3 x)

limit as x approaches 2.99 of sqrt(1+x)

x \to 2.99 lim (1 + x)

integral of 1/(sqrt(1+\sqrt{1+x))}

\int \frac{1}{1 + 1 + x} d x

derivative of 3x^2-6 derivative of

3 x^{2} - 6

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)