# How do you find the derivatives of #s=roott(t)# by logarithmic differentiation?

Please see the explanation.

Rewrite as:

Use the natural logarithm on both sides:

Differentiate both sides:

Multiply both sides by s:

Substitute for s:

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To find the derivative of ( s = \sqrt{t} ) using logarithmic differentiation, follow these steps:

- Take the natural logarithm of both sides of the equation: ( \ln(s) = \ln(\sqrt{t}) ).
- Use the properties of logarithms to simplify the right side of the equation: ( \ln(s) = \frac{1}{2}\ln(t) ).
- Differentiate both sides of the equation with respect to ( t ).
- Apply the chain rule and the derivative of the natural logarithm.
- Solve for ( \frac{ds}{dt} ).

The result will be ( \frac{ds}{dt} = \frac{1}{2s} ).

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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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