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

The Power Rule and the Chain Rule must be applied to this problem.

First, we take the radical (square root) and transform it into its exponential form.

Use the Chain Rule.

Change the exponents from negative to positive.

Convert the radical form of a positive exponent.

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To find the derivative of (y = \sqrt{x-1}), we can use the power rule for differentiation. The square root function can also be written as (y = (x-1)^{1/2}). Applying the power rule, the derivative is:

[ \frac{dy}{dx} = \frac{1}{2}(x-1)^{-1/2} \times 1 = \frac{1}{2\sqrt{x-1}} ]

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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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