If `Y = sX and Z = tX`, where all the letters denotes the functions of x and suffixes denotes the differentiation wr.t x then prove that `|(X,Y,Z),(X_1,Y_1,Z_1),(X_2,Y_2,Z_2)|=X^3|(s_1,t_1),(s_2,t_2)|`

If y = SX and z = tX where all the letters denotes the functions of x and suffixes denotes the differentiation w.r.t x and |(X,Y,Z),(X_1,Y_1,Z_1),(X_2,Y_2,Z_2)|=X^(k) |(S_1,t_1),(S_2,t_2)| then K is

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

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,Z),(X_(1),Y_(1),Z_(1)),(X_(2),Y_(2),Z_(2)):}|+|{:(S_(1),t_(1)),(S_(2),t_(2)):}|=X^(n) , then n=

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=

If Y=sX and Z =tX all the varibles beings functions of x then prove that |{:(X,Y,Z),(X_(1),Y_(1),Z_(1)),(X_(2),Y_(2),Z_(2)):}| =X^(3) |{:(s_(1),t_(1)),(s_(2),t_(2)):}| where suffixes denote the order of differention with respect to x.

If Y=sX and Z =tX all the varibles beings functions of x then prove that |{:(X,Y,Z),(X_(1),Y_(1),Z_(1)),(X_(2),Y_(2),Z_(2)):}| =X^(3) |{:(s_(1),t_(1)),(s_(2),t_(2)):}| where suffixes denote the order of differention with respect to x.

If Y=sX and Z =tX all the varibles beings functions of x then prove that |{:(X,Y,Z),(X_(1),Y_(1),Z_(1)),(X_(2),Y_(2),Z_(2)):}| =X^(3) |{:(s_(1),t_(1)),(s_(2),t_(2)):}| where suffixes denote the order of differention with respect to x.

Prove that |(1,x,x^2),(1,y,y^2),(1,z,z^2)|=(x-y)(y-z)(z-x)

Prove that |(1,x,x^2),(1,y,y^2),(1,z,z^2)| = (x-y)(y-z)(z-x)