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Find (dy)/(dx) when y= (x^(log x)) ( ...

Find ` (dy)/(dx) ` when ` y= (x^(log x)) ( log x)^(x), x gt 1`

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To find \(\frac{dy}{dx}\) for the function \(y = (x^{\log x})(\log x)^{x}\) where \(x > 1\), we will follow these steps: ### Step 1: Take the natural logarithm of both sides We start by taking the logarithm of both sides to simplify the differentiation process. \[ \log y = \log\left((x^{\log x})(\log x)^{x}\right) \] ...
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