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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

f (x) = 9 - 16 x

\int (8 x^{7} + 9) x^{8} + 9 x d x

y = \frac{8}{x ^{2}}

\frac{d}{d x} (16 e^{2 x})

y = 3 arccos (\frac{x}{2})

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