`Delta_(1)=|{:(x,b,b),(a,x,b),(a,a,x):}|` and `Delta_(2)=|{:(x,b),(a,x):}|` are the given determinations then

Options

A. `Delta_(1)=3(Delta_(2))^(2)`
B. `(d)/(dx)(Delta_(1))=3Delta_(2)`
C. `(d)/(dx)(Delta_(1))=3(Delta_(2))^(2)`
D. `Delta_(1)=3Delta_(2)^(3//2)`

Answer

B

Explanation

`(b)` `Delta_(1)=x(x^(2)-ab)-b(ax-ab)+b(a^(2)-ax)`
`=x^(3)-3abx+ab^(2)+a^(2)b`
`:.(d)/(dx)(Delta_(1))=3x^(2)-3ab=3(x^(2)-ab)=3Delta_(2)`