Is the function $$ \log \log |\sin x|$$ differentiable? How can I justify the answer?
2026-04-29 07:28:17.1777447697
Is this composite function differentiable?
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If $x$ can be complex and defined appropriately, the Chain Rule would work to produce the derivative in a reasonable sense.
If $x$ is intended to be real, however, since $\log |\sin x| < 1$, the function is undefined, and hence not differentiable.