If $straight x space equals space straight e to the power of straight y plus straight e to the power of straight y plus.... to space infinity end exponent space comma space straight x space greater than thin space 0 comma space then space dy over dx space is$

x /x+1

x-1/x

1/x

x+1/x

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Solution

x-1/x

straight x space equals space straight e to the power of straight y plus straight e to the power of straight y plus.... infinity end exponent end exponent straight x space equals straight e to the power of straight y plus straight x end exponent Taking space log space on space both space side log space straight x space equals space straight y plus straight x Diff. space straight w. straight r. straight t space to space straight x 1 over straight x space equals dy over dx plus 1 rightwards double arrow dy over dx space equals space fraction numerator 1 minus straight x over denominator straight x end fraction

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