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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Power Rule:

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

= - (- 1 \cdot x^{- 1 - 1})

Simplify

- (- 1 \cdot x^{- 1 - 1}) : \frac{1}{x ^{2}}

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

\int x^{2} cos (x y) d y

f (t) = e^{4 t}

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

t \to 0 lim (\frac{6 e ^{t} - 6}{t})

\int - e^{x} cos (x) d x

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