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If y=log (1+ sin x), prove that y(4)+y(...

If y=log (1+ sin x), prove that `y_(4)+y_(3)y_(1)+y_(2)^(2)=0`.

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To prove that \( y^{(4)} + y^{(3)}y^{(1)} + (y^{(2)})^2 = 0 \) for \( y = \log(1 + \sin x) \), we will find the first four derivatives of \( y \) and substitute them into the equation. ### Step 1: Find the first derivative \( y' \) Given: \[ y = \log(1 + \sin x) \] ...
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