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y=((x^(2))/(x+1))^(x)...

`y=((x^(2))/(x+1))^(x)`

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To solve the problem \( y = \left(\frac{x^2}{x+1}\right)^x \), we will use logarithmic differentiation. Here’s a step-by-step solution: ### Step 1: Take the natural logarithm of both sides We start by taking the natural logarithm of both sides of the equation: \[ \ln y = \ln\left(\left(\frac{x^2}{x+1}\right)^x\right) \] ...
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