Derivative of \( \cos^{-1}\left( \frac{\sin x + \cos x}{\sqrt{2}} \right) \), \( -\frac{\pi}{4} < x < \frac{\pi}{4} \) with respect to \( x \) is :
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Always double-check interval ranges. Since \( \cos(- \theta) = \cos(\theta) \), adapting the sign of the inside angle ensures compliance with the principal range of \( \cos^{-1} \).