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Valentin Fadeev

Going beyond dx

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Edited by Valentin Fadeev, Sunday, 18 Sept 2011, 23:23

This is quite a minor trick and like many things listed here may seem quite trivial. However, this is one of those few occasions when I had the tool in mind, before I actually got the example touse it on. Consider:

equation left hand side d times y divided by d times x equals right hand side one plus two divided by x plus y

which does not really require a great effort to solve. But forget all the standard ways for a moment and add d times x divided by d times x equals one to both parts:

equation left hand side d times open x plus y close divided by d times x equals right hand side two times one plus open x plus y close divided by x plus y

equation left hand side sum with, 3 , summands negative one plus one plus open x plus y close times d times open x plus y close divided by one plus open x plus y close equals right hand side two times d times x

equation left hand side d times open sum with, 3 , summands one plus x plus y close divided by one plus open x plus y close equals right hand side d times open y minus x close

natural log of absolute value of sum with, 3 , summands one plus x plus y equals open y minus x close plus natural log of cap c

equation left hand side sum with, 3 , summands one plus x plus y equals right hand side cap c times exp of y minus x

Hope this can be stretched to use in more complicated cases

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