# How do you find #f'(4)# if #f(x)=2sqrt(2x)#?

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To find ( f'(4) ) if ( f(x) = 2\sqrt{2x} ), you first need to find the derivative of ( f(x) ) with respect to ( x ), denoted as ( f'(x) ). Then, substitute ( x = 4 ) into the derivative function ( f'(x) ).

Using the power rule and chain rule, the derivative of ( f(x) = 2\sqrt{2x} ) with respect to ( x ) is:

[ f'(x) = \frac{d}{dx} [2\sqrt{2x}] = 2 \cdot \frac{1}{2\sqrt{2x}} \cdot \frac{d}{dx} [2x] = \frac{1}{\sqrt{2x}} \cdot 2 = \frac{2}{\sqrt{2x}} ]

Now, substitute ( x = 4 ) into ( f'(x) ):

[ f'(4) = \frac{2}{\sqrt{2 \cdot 4}} = \frac{2}{\sqrt{8}} = \frac{2}{2\sqrt{2}} = \frac{1}{\sqrt{2}} ]

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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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