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

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

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

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

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\frac{d}{d 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}}

y = 2 x^{3} + 4 x^{2} - x + 2

\int 3 x^{- 1} d x

2 x y d x + (x^{2} - 1) d y = 0

\int_{0}^{\infty} 3 y e^{- 3 y} d y

\int (sec^{4} (x)) d x

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