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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (1) = 0

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

= 0 - \frac{1}{x ^{2}}

Simplify

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

(9, 2.6), (8, 2.2)

\int sinh (2 t) d t

\int_{0}^{1} 2 x + 1 d x

\frac{5}{t ^{6}}

\int (t^{3} - 9 t) d t

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