# How do you find the derivative of #1/sqrt (x-1)#?

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To find the derivative of ( \frac{1}{\sqrt{x-1}} ), use the chain rule and the power rule.

- Rewrite the expression as ( (x-1)^{-\frac{1}{2}} ).
- Apply the power rule: ( \frac{d}{dx}(x-1)^{-\frac{1}{2}} = -\frac{1}{2}(x-1)^{-\frac{1}{2}-1} ).
- Simplify the expression: ( -\frac{1}{2}(x-1)^{-\frac{3}{2}} ).
- Therefore, the derivative of ( \frac{1}{\sqrt{x-1}} ) is ( -\frac{1}{2\sqrt{x-1}} ).

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