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

It is

You can use the chain rule and the derivative of the power.

Your function can be written as

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

[ \frac{d}{dx} \left( \frac{1}{\sqrt{x-1}} \right) = \frac{d}{dx} \left( (x-1)^{-\frac{1}{2}} \right) = -\frac{1}{2}(x-1)^{-\frac{3}{2}} ]

Therefore, the derivative of ( \frac{1}{\sqrt{x-1}} ) is ( -\frac{1}{2\sqrt{(x-1)^3}} ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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