# How do you find the derivative of #y=ln(sqrt(x))#?

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Explanation

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To find the derivative of ( y = \ln(\sqrt{x}) ), you can use the chain rule.

- First, rewrite the function using the power rule for logarithms: ( y = \frac{1}{2}\ln(x) ).
- Now differentiate ( y ) with respect to ( x ), applying the chain rule and the derivative of the natural logarithm function: [ \frac{dy}{dx} = \frac{1}{2} \cdot \frac{1}{x} \cdot \frac{dx}{dx} ]
- Since ( \frac{dx}{dx} = 1 ), the expression simplifies to: [ \frac{dy}{dx} = \frac{1}{2x} ]

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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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