If y=[(x+1)(2 x+1)(3 x+1) ( n x+1)]^4 then d y ~d x at x=0 is

Step-by-step solution

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