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If e^y(x+1)=1, show that (d^2y)/(dx^2)=(...

If `e^y(x+1)=1`, show that `(d^2y)/(dx^2)=((dy)/(dx))^2`.

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To solve the problem, we need to show that if \( e^{y}(x + 1) = 1 \), then \( \frac{d^2y}{dx^2} = \left(\frac{dy}{dx}\right)^2 \). ### Step 1: Start with the given equation We have: \[ e^{y}(x + 1) = 1 \] ...
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