What is (\partial)/(\partial x)((x-a)^{-1}) ?

The answer to (\partial)/(\partial x)((x-a)^{-1}) is -1/((x-a)^2)

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(\partial)/(\partial x)((x-a)^{-1})

\frac{\partial}{\partial x} ((x - a)^{- 1})

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

Solution steps

\frac{\partial}{\partial x} ((x - a)^{- 1})

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x - a) = 1

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

Simplify

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

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What is (\partial)/(\partial x)((x-a)^{-1}) ?
The answer to (\partial)/(\partial x)((x-a)^{-1}) is -1/((x-a)^2)