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

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The derivative of the expression is

That is, the derivative of the outer function evaluated at the inner function times the derivative of the inner function

Evaluating the outer function is the straightforward application of the rules of polynomial differentiation applied to its index, that is

Or, if you prefer, reverting to the square root notation and noting the negative index

So the overall derivative is

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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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