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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

d er i v a t i v e f (x) = lo g_{2} (3 x)

in v erse l a pl a ce \frac{s - 1}{s ^{2} ( s + 3 )}

t \to a lim (t)

t an g e n t x^{2} - 2 x

d er i v a t i v e 7 x^{2} - 8 x + 3

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