If 8 f (x)+6 f ( 1 x )=x+5 and y=x^2 f (x) , then d y ~d x at x=-1 is

Step-by-step solution

8 f(x)+6 f ( 1 x )=x+5...(i) Differentiating w.r.t. x , we get 8 f^ (x)+6 f^ ( 1 x ) ( -1 x^2 )=1...(ii) Substituting x=-1 in (i), we get 8 f(-1)+6 f(-1)=4 array ll & 14 f(-1)=4 & f(-1)= 4 14 = 2 7 ...(iii) array Substituting x=-1 in (ii), we get aligned & f ^ (-1)= 1 2 . & y=x^2 f (x) aligned ...(iv) aligned d y ~d x & =2 . ~d y ~d x |_ x=-1 & =2(-1)+x^2 f ^ (x) & = -4 7 + 1 2 [ From (iii) and (iv) ] & =- 1 14 aligned