What is (\partial)/(\partial x)(1/((x-2)^2)) ?

The answer to (\partial)/(\partial x)(1/((x-2)^2)) is -2/((x-2)^3)

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(\partial)/(\partial x)(1/((x-2)^2))

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

- \frac{2}{( x - 2 ) ^{3}}

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

- \frac{2}{( x - 2 ) ^{3}} \frac{\partial}{\partial x} (x - 2)

= - \frac{2}{( x - 2 ) ^{3}} \frac{\partial}{\partial x} (x - 2)

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

= - \frac{2}{( x - 2 ) ^{3}} \cdot 1

Simplify

= - \frac{2}{( x - 2 ) ^{3}}

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What is (\partial)/(\partial x)(1/((x-2)^2)) ?
The answer to (\partial)/(\partial x)(1/((x-2)^2)) is -2/((x-2)^3)