What is the derivative of 1/((x-5)^2) ?

The derivative of 1/((x-5)^2) is -2/((x-5)^3)

What is the first derivative of 1/((x-5)^2) ?

The first derivative of 1/((x-5)^2) is -2/((x-5)^3)

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derivative of

\frac{1}{( x - 5 ) ^{2}}

- \frac{2}{( x - 5 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{1}{( x - 5 ) ^{2}})

Apply exponent rule:

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

= \frac{d}{d x} ((x - 5)^{- 2})

Apply the chain rule:

- \frac{2}{( x - 5 ) ^{3}} \frac{d}{d x} (x - 5)

= - \frac{2}{( x - 5 ) ^{3}} \frac{d}{d x} (x - 5)

\frac{d}{d x} (x - 5) = 1

= - \frac{2}{( x - 5 ) ^{3}} \cdot 1

Simplify

= - \frac{2}{( x - 5 ) ^{3}}

What is the derivative of 1/((x-5)^2) ?
The derivative of 1/((x-5)^2) is -2/((x-5)^3)
What is the first derivative of 1/((x-5)^2) ?
The first derivative of 1/((x-5)^2) is -2/((x-5)^3)