Differentiation Question 138
Question: If $ \frac{d}{dx}( \frac{1+x^{4}+x^{8}}{1+x^{2}+x^{4}} )=ax^{3}+bx, $ then
Options:
A) $ a=4,b=2 $
B) $ a=4,b=-2 $
C) $ a=-2,b=4 $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
[b] We have, $ \frac{d}{dx}[ \frac{(1+x^{2}+x^{4})(1-x^{2}+x^{4})}{(1+x^{2}+x^{4})} ]=ax^{3}+bx $
$ \Rightarrow \frac{d}{dx}(1-x^{2}+x^{4})=ax^{3}+bx $
$ \Rightarrow -2x+4x^{3}=ax^{3}+bx $
$ \Rightarrow a=4 $ and $ b=-2. $
BETA
