If \( f(x)=\left.|x|\right|^{\text {sinx }} \mid \), then \( f^{\prime}(\pi / 4) \) is equal to
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If \( f(x)=\left.|x|\right|^{\text {sinx }} \mid \), then \( f^{\prime}(\pi / 4) \) is equal to
(1) \( \left(\frac{\pi}{4}\right)^{1 / \sqrt{2}}\left(\frac{\sqrt{2}}{2} \ell \mathrm{n} \frac{4}{\pi}-\frac{2 \sqrt{2}}{\pi}\right) \)
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(2) \( \left(\frac{\pi}{4}\right)^{1 / \sqrt{2}}\left(\frac{\sqrt{2}}{2} \ell \operatorname{n} \frac{4}{\pi}+\frac{2 \sqrt{2}}{\pi}\right) \)
(3) \( \left(\frac{\pi}{4}\right)^{1 / \sqrt{2}}\left(\frac{\sqrt{2}}{2} \ell \mathrm{n} \frac{\pi}{4}-\frac{2 \sqrt{2}}{\pi}\right) \)
(4) \( \left(\frac{\pi}{4}\right)^{1 / \sqrt{2}}\left(\frac{\sqrt{2}}{2} \ln \frac{\pi}{4}+\frac{2 \sqrt{2}}{\pi}\right) \)
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