NDA2022MathematicsDifferentiationActual
If d d x ( 1+x^4+x^8 1-x^2+x^4 )=a x+b x^3 , then which one of the following is correct?
Options
- Aa=b
- Ba=2 b
- Ca+b=0
- D2 a=b
Correct answer
D. 2 a=b
Step-by-step solution
aligned & Let f(x)= x^8+x^4+1 x^4-x^2+1 & = x^8+2 x^4+1-x^4 x^4-x^2+1 = (x^4+1 )^2- (x^2 )^2 (x^4-x^2+1 ) & = (x^4-x^2+1 ) (x^4+x^2+1 ) x^4-x^2+1 & f(x)=x^4+x^2+1 & f^ (x)=4 x^3+2 x=a x+b x^3 & a=2, b=4 b=2 a aligned