If A= | array lll x & 1 & 1 1 & x & 1 1 & 1 & x array | and B= | array cc x & 1 1 & x array | , then d A d x is equal to

Step-by-step solution

array ll Given, & A= | array lll x & 1 & 1 1 & x & 1 1 & 1 & x array | & A=x (x²-1 )-(x-1)+(1-x) & A=x³-x-x+1+1-x & A=x³-3 x+2 array On differentiating w.r.t. x , we get d A d x =3 x²-3..(i) Also, given B= | array ll x & 1 1 & x array | array cc & B=x²-1 & 3 B=3 x²-3...(ii) array From Eqs. (i) and (ii), we get d A d x =3 B