Functions Question 598
Question: Function $ y={{\sin }^{-1}}( \frac{2x}{1+x^{2}} ) $ is not differentiable for
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Options:
A) $ |x|,<1 $
B) $ x=1,-1 $
C) $ |x|,>1 $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ y’=\frac{1}{\sqrt{1-{{( \frac{2x}{1+x^{2}} )}^{2}}}}.\frac{2(1+x^{2})-4x^{2}}{{{(1+x^{2})}^{2}}}=\frac{2(1-x^{2})}{\sqrt{{{(1-x^{2})}^{2}}.(1+x^{2})}} $
Þ $ y’= \begin{cases} & \frac{2}{1+x^{2}}for|x|<1 \\ & \frac{-2}{1+x^{2}}for|x|>1 \\ \end{cases} . $ Hence for $ |x|=1 $ , the derivative does not exist.
BETA
