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Mr Davis 97

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- Thread starter Mr Davis 97
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In summary, the conversation discusses the expression ##e^{\frac{1}{2} \log|2x-1|}## and the possibility of simplifying it to ##\sqrt{2x-1}##. However, there is uncertainty about justifying this simplification, as it would result in a different domain for the function. The conversation also mentions taking the derivative of the expression, which would be problematic regardless of the approach due to the function's non-differentiability at ##x = \frac{1}{2}##.

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Mr Davis 97

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Was there something wrong with ##\sqrt{|2x-1|}##?

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Mr Davis 97

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Well, I then need to take the derivative of the resulting expression, and I don't see how to take the derivative of ##\sqrt{|2x-1|}##Orodruin said:Was there something wrong with ##\sqrt{|2x-1|}##?

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JonnyG

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Regardless of how you do things, your function will not be differentiable in x=1/2.Mr Davis 97 said:Well, I then need to take the derivative of the resulting expression, and I don't see how to take the derivative of ##\sqrt{|2x-1|}##

An exponential with a square root is an expression where the variable is raised to a power that is also a fraction with a numerator of 1 and a denominator of 2. This is commonly written as x^(1/2) or √x.

Simplifying an exponential with a square root can help make the expression easier to work with and understand. It can also help to identify patterns and relationships between different exponential expressions.

To simplify an exponential with a square root, you can use the exponent rules for radicals. If the exponent is a fraction, you can rewrite it as a radical and then apply the appropriate rules. For example, x^(1/2) can be rewritten as √x and then simplified further if needed.

One common mistake is forgetting to apply the exponent rules for radicals and trying to simplify the expression as a regular exponential. Another mistake is incorrectly applying the rules and getting the wrong simplified expression.

It is not possible to simplify an exponential with a square root when the exponent is a fraction with a denominator other than 2. In this case, the expression cannot be rewritten as a radical and the exponent rules for radicals cannot be applied.

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