A) \[\cos \,\left( \frac{1}{x} \right)+2x\sin \left( \frac{1}{x} \right)\]
B) \[2x\sin \left( \frac{1}{x} \right)-\cos \left( \frac{1}{x} \right)\]
C) \[\cos \left( \frac{1}{x} \right)-2x\sin \left( \frac{1}{x} \right)\]
D) None of these
Correct Answer: B
Solution :
\[\frac{d}{dx}\left( {{x}^{2}}\sin \frac{1}{x} \right)={{x}^{2}}\cos \left( \frac{1}{x} \right)\frac{d}{dx}\left( \frac{1}{x} \right)\]\[+2x\sin \left( \frac{1}{x} \right)\] \[=-\frac{1}{{{x}^{2}}}.{{x}^{2}}\cos \left( \frac{1}{x} \right)+2x\sin \left( \frac{1}{x} \right)=2x\sin \left( \frac{1}{x} \right)-\cos \left( \frac{1}{x} \right)\].
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