If y=(1+x) (1+x^2 ) (1+x^4 ) (1+x^8 ) (1+x¹⁶ ) then what is d y d x at x=0 equal to?

Step-by-step solution

aligned & y=(1+x)(1+x)^2 (1+x^4 ) (1+x^8 ) (1+x¹⁶ ) & y= (1+x)+ (1+x^2 )+ (1+x^4 )+ (1+x^8 ) & + (1+x¹⁶ ) & 1 y d y d x = 1 1-x + 2 x 1+x^2 + 4 x^3 1+x^4 + 8 x^7 1+x^8 + 16 x¹⁵ 1+x¹⁶ & d y d x =y [ 1 1+x + 2 x 1+x^2 + 4 x^3 1+x^4 + 8 x^7 1+x^8 + 16 x¹⁵ 1+x¹⁶ ] aligned Put x=0 d y d x =1[1+0+0+0+0]=1