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

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

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

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

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derivative of

(x - 2)^{- 1}

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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