If `Y=SX`, `Z=tX` all the variables being differentiable functions of `x` and lower suffices denote the derivative with respect to `x` and `|{:(X,Y,X),(X_(1),Y_(1),Z_(1)),(X_(2),Y_(2),Z_(2)):}|+|{:(S_(1),t_(1)),(S_(2),t_(2)):}|=X^(n)`, then `n=`

Options

A. `1`
B. `2`
C. `3`
D. `4`

Answer

C

Explanation

`(c )` `Delta=|{:(X,SX,tX),(X_(1),SX_(1)+S_(1)X,tX_(1)+t_(1)X),(X_(2),SX_(2)+2S_(1)X_(1)+S_(2)X,tX_(2)+2t_(1)X_(1)+t_(2)X):}|`
`({:(C_(2)toC_(2)-SC_(1)),(C_(3)toC_(3)-tC_(1)):})`
`=|{:(X,0,0),(X_(1),S_(1)X,t_(1)X),(X_(2),2S_(1)X_(1)+S_(2)X,2t_(1)X_(1)+t_(2)X):}|`
`=X^(2)|{:(S_(1),t_(1)),(2S_(1)X_(1)+S_(2)X,2t_(1)X_(1)+t_(2)X):}|`
`=X^(3)|{:(S_(1),t_(1)),(S_(2),t_(2)):}|(R_(2)toR_(2)-2X_(1)R_(1))`
`:.n=3`