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Q.

If y=sin-12x1+x2, then which of the following is not correct ?

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a

dydx=21+x2 for |x|<1

b

dydx=-21+x2 for |x|>1

c

dydx=2 for x=-1

d

dydx does not exist at |x|=1

answer is D.

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Detailed Solution

y=sin−12x1+x2=2 tan−1x                           if x≤1π−2tan−1x        if x>1  ∴If x≤1⇒dydx=21+x2and if |x|>1⇒dydx=−21+x2
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