# How do you find f'(x) using the limit definition given #4/(sqrt(x))#?

by definition

here

multiply by the conjugate

start to combine terms

setting h = 0

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To find ( f'(x) ) using the limit definition, you apply the definition of the derivative, which is ( f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h} ). For the function ( f(x) = \frac{4}{\sqrt{x}} ), substitute ( f(x + h) ) and ( f(x) ) into the limit definition, and simplify to find the derivative.

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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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