If \( f(x)=|x|^{|\sin x|} \), then \( f^{\prime}\left(-\frac{\pi}{4}\right) \) equals (A) \( \le...
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0If \( f(x)=|x|^{|\sin x|} \), then \( f^{\prime}\left(-\frac{\pi}{4}\right) \) equals
(A) \( \left(\frac{\pi}{4}\right)^{1 / \sqrt{2}}\left(\frac{\sqrt{2}}{2} \ln \frac{4}{\pi}-\frac{2 \sqrt{2}}{\pi}\right) \)
(B) \( \left(\frac{\pi}{4}\right)^{1 / \sqrt{2}}\left(\frac{\sqrt{2}}{2} \ln \frac{4}{\pi}+\frac{2 \sqrt{2}}{\pi}\right) \)
(C) \( \left(\frac{\pi}{4}\right)^{1 / \sqrt{2}}\left(\frac{\sqrt{2}}{2} \ln \frac{\pi}{4}-\frac{2 \sqrt{2}}{\pi}\right) \)
(D) \( \left(\frac{\pi}{4}\right)^{1 / \sqrt{2}}\left(\frac{\sqrt{2}}{2} \ln \frac{\pi}{4}+\frac{2 \sqrt{2}}{\pi}\right) \)
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