# How do you find f'(x) using the definition of a derivative for #f(x)= x - sqrt(x) #?

Use limit definition of derivative to find:

#f'(x) =1+1/(2sqrt(x))#

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To find (f'(x)) using the definition of a derivative for (f(x) = x - \sqrt{x}), you use the definition of the derivative, which is given by the limit:

[ f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} ]

Substitute (f(x) = x - \sqrt{x}) into the definition of the derivative and simplify. Then, evaluate the limit as (h) approaches (0). The result will be the derivative (f'(x)).

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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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