If y= ((x+1)(4 x+1)(9 x+1) ( n ^2 x+1 ) )^2 , then dy d x at x=0 is

Step-by-step solution

array ll y= & ((x+1)(4 x+1)(9 x+1) ( n ^2 x+1 ) )^2 & y=2[ (x+1)+ (4 x+1)+ (9 x+1) & .+ + ( n ^2 x+1 ) ] array Differentiating w.r.t. x , we get 1 y ~d y ~d x =2 [ 1 (x+1) + 4 4 x+1 + 9 9 x+1 + + n ^2 n ^2 x +1 ] d y ~d x =2 y [ (1)^2 x+1 + (2)^2 4 x+1 + (3)^2 9 x+1 + + n ^2 n ^2 x+1 ] aligned . d y ~d x |_ x=0 & =2 y(0) [1^2+2^2+3^2+ + n ^2 ] & =2(1) n ( n +1)(2 n +1) 6 & = n ( n +1)(2 n +1) 3 aligned