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If $y^2 + \log_e(\cos^2 x) = y$, $x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$, then:
(1) $y’’(0) = 0$ (2) $|y’(0)| + |y’’(0)| = 1$ (3) $|y’’(0)| = 2$ (4) $|y’(0)| + |y’’(0)| = 3$
Differentiating: $2yy’ - 2\tan x = y’$. At $x = 0$: $y’(0) = 0$. Differentiating again and putting $x = 0$: $y’’(0) = 2$.
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