What is (\partial)/(\partial x)((1+x^{-1})^2) ?

The answer to (\partial)/(\partial x)((1+x^{-1})^2) is -(2(x+1))/(x^3)

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(\partial)/(\partial x)((1+x^{-1})^2)

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{\partial}{\partial 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{x ^{2}}{1} d x

\int_{0}^{7} x^{2} - 6 x + 5 d x

\int 2 e^{2 x} sin (2 x) d x

\frac{d}{d x} ((2 x^{2} + 3)^{2})

\frac{2}{s + 1} + 8 a \cdot \frac{s}{s ^{2} + 9}

What is (\partial)/(\partial x)((1+x^{-1})^2) ?
The answer to (\partial)/(\partial x)((1+x^{-1})^2) is -(2(x+1))/(x^3)