A) \[a=4,b=2\]
B) \[a=4,b=-2\]
C) \[a=-2,b=4\]
D) None of these
Correct Answer: B
Solution :
[b] We have, \[\frac{d}{dx}\left[ \frac{(1+{{x}^{2}}+{{x}^{4}})(1-{{x}^{2}}+{{x}^{4}})}{(1+{{x}^{2}}+{{x}^{4}})} \right]=a{{x}^{3}}+bx\] \[\Rightarrow \frac{d}{dx}(1-{{x}^{2}}+{{x}^{4}})=a{{x}^{3}}+bx\] \[\Rightarrow -2x+4{{x}^{3}}=a{{x}^{3}}+bx\] \[\Rightarrow a=4\] and \[b=-2.\]
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