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

The derivative of f(x)=(-x^2-1)/((x^2-1)^2) is -(2x(-x^2-3))/((x^2-1)^3)

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

The first derivative of f(x)=(-x^2-1)/((x^2-1)^2) is -(2x(-x^2-3))/((x^2-1)^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= - \frac{2 x ( - x ^{2} - 3 )}{( x ^{2} - 1 ) ^{3}}

\int tan^{3} (19 π x) d x

\frac{1}{1 + x}

\int x - y d x

x \to \infty lim (x^{3} sin (\frac{1}{x}))

arctan (6 y^{5} + 1)

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