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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d x}{d x} = 1

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

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

x \to + 0 lim (\frac{3 x}{x e ^{x}})

\frac{\partial}{\partial y} (x^{3} y - y^{4})

\frac{d}{d x} (arcsin (9 x^{4}))

y^{^{''}} = 2 t^{2}

\frac{d}{d y} (\frac{6 x + y}{8 z - 5 y})

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