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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int_{1}^{5} 6 x ln (x) d x

\int cos (x + n x) d x

\frac{d y}{d t} = y sin (t)

\int \frac{5 + u}{u} d u

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