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If x^y=e^(x-y), prove that (dy)/(dx)=(lo...

If `x^y=e^(x-y)`, prove that `(dy)/(dx)=(logx)/(1+logx)^2`

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To solve the problem, we need to differentiate the equation \( x^y = e^{(x - y)} \) and prove that \( \frac{dy}{dx} = \frac{\log x}{(1 + \log x)^2} \). ### Step-by-Step Solution: 1. **Take the natural logarithm of both sides**: \[ \log(x^y) = \log(e^{(x - y)}) \] ...
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