y=(1+x) (1+x^2 ) (1+x^4 ) (1+x^ 2 n ) , then the value of d y d x at x=0 is

Step-by-step solution

y=(1+x) (1+x^2 ) (1+x^4 ) (1+x^ 2 n ) Taking ' ' on both sides, we get aligned y= (1+x)+ (1+x^2 ) & + (1+x^4 ) & + + (1+x^ 2 n ) aligned Differentiating w.r.t. x , we get 1 y d y ~d x = 1 1+x + 2 x 1+x^2 + 4 x^3 1+x^4 + + 2 n x^ 2 n -1 1+x^ 2 n At x=0 , (i) y=1 ( . ii) . d y ~d x |_ x=0 =1+0+0+ +0=1