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Continuity And Differentiability

Question

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Differentiate the following w.r.t.x: $log open parentheses fraction numerator 1 plus straight x over denominator 1 minus straight x end fraction close parentheses$

Solution

Let space straight y equals log open parentheses fraction numerator 1 plus straight x over denominator 1 minus straight x end fraction close parentheses therefore space straight y equals log left parenthesis 1 plus straight x right parenthesis minus log left parenthesis 1 minus straight x right parenthesis therefore space dy over dx equals fraction numerator 1 over denominator 1 plus straight x end fraction minus fraction numerator 1 over denominator 1 minus straight x end fraction left parenthesis negative 1 right parenthesis equals fraction numerator 1 over denominator 1 plus straight x end fraction plus fraction numerator 1 over denominator 1 minus straight x end fraction equals fraction numerator 1 minus straight x plus 1 plus straight x over denominator left parenthesis 1 plus straight x right parenthesis left parenthesis 1 minus straight x right parenthesis end fraction equals fraction numerator 2 over denominator 1 minus straight x squared end fraction

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