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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derivative of

(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}}

\int \frac{1}{x ^{2}} 3 + \frac{1}{x} d x

\frac{d}{d x} (sin (ln (2 x)))

\int t sec^{2} (3 t) d t

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

\int \frac{e ^{x^{2}}}{x ^{2}} d x

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)