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`"If "y=a^(x^(a^(x...oo)))", prove that "(dy)/(dx)=(y^(2)(logy))/(x[1-y(logx)(logy)]).`

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To solve the problem, we are given the equation \( y = a^{x^{a^{x^{\cdots}}}} \) and we need to prove that \[ \frac{dy}{dx} = \frac{y^2 \log y}{x(1 - y \log x \log y)}. \] ### Step-by-Step Solution: ...
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