InterviewSolution
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InterviewSolution
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If `y = x^(x ^(x^(x ^(x.... oo)` then prove that ` x dy/dx = y^2/(1- y logx )` |
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Answer» We know that an infinite series is not affected by the exclusion of a single term. So, we may write the given function as `y=x^(y).` Now, `y=x^(y)rArr logy=y log x`. On differentiating both sides of (i) w.r.t. x, we get `(1)/(y).(dy)/(dx)=y.(1)/(x)+logx.(dy)/(dx)` `rArr((1)/(y)-logx)(dy)/(dx)=(y)/(x)` `rArr((1-ylogx))/(y).(dy)/(dx)=(y)/(x)` `(dy)/(dx)={(y)/(x)xx(y)/((1-y logx))}rArr (dy)/(dx)=(y^(2))/(x(1-ylogx)).` |
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