How do you differentiate #f(x)=[2(ln x)]/sqrtx#?
According to the Quotient Rule:
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To differentiate ( f(x) = \frac{2\ln x}{\sqrt{x}} ), apply the quotient rule, which states:
[ \frac{d}{dx}\left(\frac{u}{v}\right) = \frac{u'v - uv'}{v^2} ]
Let ( u = 2\ln x ) and ( v = \sqrt{x} ). Then differentiate each term:
[ u' = \frac{2}{x} ] [ v' = \frac{1}{2\sqrt{x}} ]
Substitute these into the quotient rule:
[ f'(x) = \frac{(2)(1)\sqrt{x} - (2\ln x)\left(\frac{1}{2\sqrt{x}}\right)}{(\sqrt{x})^2} ]
[ f'(x) = \frac{2\sqrt{x} - \frac{\ln x}{\sqrt{x}}}{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.
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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