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}})

Simplify

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

y^{^{'}} - \frac{3}{x} y = \frac{y ^{4}}{x ^{2}}

\frac{d}{d s} (s i)

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

\int sin (x) cos (n) x d x

y^{^{'}} = \frac{t}{1 + t ^{2}} \cdot e^{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)