Differentiation Question 69
Question: $ \frac{d}{dx}( x^{2}\sin \frac{1}{x} )= $
Options:
A) $ \cos ( \frac{1}{x} )+2x\sin ( \frac{1}{x} ) $
B) $ 2x\sin ( \frac{1}{x} )-\cos ( \frac{1}{x} ) $
C) $ \cos ( \frac{1}{x} )-2x\sin ( \frac{1}{x} ) $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ \frac{d}{dx}( x^{2}\sin \frac{1}{x} )=x^{2}\cos ( \frac{1}{x} )\frac{d}{dx}( \frac{1}{x} ) $
$ +2x\sin ( \frac{1}{x} ) $
$ =-\frac{1}{x^{2}}.x^{2}\cos ( \frac{1}{x} )+2x\sin ( \frac{1}{x} )=2x\sin ( \frac{1}{x} )-\cos ( \frac{1}{x} ) $ .
BETA
