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JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1
If f(x)=∣x∣∣sin⁡x∣f(x)=|x|^{|\sin x|}, then f′(−π4)f^{\prime}\left(-\frac{\pi}{4}\right) equals
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Correct option: A
(π4)1/2(22ln⁡4π−22π)\left(\frac{\pi}{4}\right)^{1 / \sqrt{2}}\left(\frac{\sqrt{2}}{2} \ln \frac{4}{\pi}-\frac{2 \sqrt{2}}{\pi}\right)
Option A is correct because it is the result of differentiating the given function and evaluating at the specified point, considering the absolute value.

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