y= [3] 1+3 x [4] 1+4 x [5] 1+5 x [7] 1+7 x [8] 1+8 x . Then d y ~d x at x=0 is

Step-by-step solution

y= [3] 1+3 x [4] 1+4 x [5] 1+5 x [7] 1+7 x [8] 1+8 x y= 1 3 (1+3 x)+ 1 4 (1+4 x) aligned + 1 5 (1+5 x) & - 1 7 (1+7 x) & - 1 8 (1+8 x) aligned Differentiating both sides w.r.t. x , we get array r 1 y d y ~d x = 1 3 1 1+3 x 3+ 1 4 1 1+4 x 4+ 1 5 1 1+5 x 5 - 1 7 1 1+7 x 7- 1 8 1 1+8 x 8 array aligned & 1 y d y ~d x = 1 1+3 x + 1 1+4 x + 1 1+5 x - 1 1+7 x - 1 1+8 x & 1 1 ( d y ~d x )_ x=0 = 1 1+0 + 1 1+0 + 1 1+0 - 1 1+0 - 1 1+0 & [ At x=0, y=1] aligned ( d y ~d x )_ x=0 =1