logarithmic

# logarithmic - Logarithmic Differentiation There is one last...

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Logarithmic Differentiation There is one last topic to discuss in this section. Taking the derivatives of some complicated functions can be simplified by using logarithms. This is called logarithmic differentiation . It’s easiest to see how this works in an example. Example 1 Differentiate the function. Solution Differentiating this function could be done with a product rule and a quotient rule. However, that would be a fairly messy process. We can simplify things somewhat by taking logarithms of both sides. Of course, this isn’t really simpler. What we need to do is use the properties of logarithms to expand the right side as follows. This doesn’t look all the simple. However, the differentiation process will be simpler. What we need to do at this point is differentiate both sides with respect to x . Note that this is really implicit differentiation .

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To finish the problem all that we need to do is multiply both sides by y and the plug in for y since we do know what that is. Depending upon the person, doing this would probably be slightly easier than doing both the
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## This note was uploaded on 11/06/2011 for the course MATH 151 taught by Professor Sc during the Fall '08 term at Rutgers.

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logarithmic - Logarithmic Differentiation There is one last...

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