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

The derivative of ((x^2+2x+1)/((x^2-2x+1))) is -(4(x+1))/((x-1)^3)

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

The first derivative of ((x^2+2x+1)/((x^2-2x+1))) is -(4(x+1))/((x-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{( x ^{2} + 2 x + 1 )}{( x ^{2} - 2 x + 1 )})

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

y^{^{'}} = - a \cdot y^{2}

\frac{d}{d t} (t^{9} e^{t})

4^{^{'}}

\frac{d}{d x} (sin (4 x^{2} + 3 x))

\int \frac{8}{x 64 - ( ln ( x ) ) ^{2}} d x

What is the derivative of ((x^2+2x+1)/((x^2-2x+1))) ?
The derivative of ((x^2+2x+1)/((x^2-2x+1))) is -(4(x+1))/((x-1)^3)
What is the first derivative of ((x^2+2x+1)/((x^2-2x+1))) ?
The first derivative of ((x^2+2x+1)/((x^2-2x+1))) is -(4(x+1))/((x-1)^3)