If f (x)=(1+x) (1+x^2 ) (1+x^4 ) (1+x^8 ) , then f^ (1)=

Step-by-step solution

y=(1+x) (1+x^2 ) (1+x^4 ) (1+x^8 )...(i) Taking 'log' on both sides, we get aligned & y= (1+x)+ (1+x^2 )+ (1+x^4 ) &+ (1+x^8 ) aligned Differentiating w.r.t. x , we get 1 ~d y y = 1 1+x + 2 x 1+x^2 + 4 x^3 1+x^4 + 8 x^7 1+x^8 ...(ii) At x=1 , (i) y=16 (ii) ( d y ~d x )_ x=1 =16 ( 1 2 + 2 2 + 4 2 + 8 2 )=120