if y= sin mx, them the value of the determinant
`|{:(y,,y_(1),,y_(2)),(y_(3),,y_(4),,y_(5)),(y_(6),,y_(7),,y_(8)):}|" Where " y_(n)=(d^(n)y)/(dx^(n)) " is "`

y = e^(ax) then (d^(n)y)/(dx^(n)) = y_(n) is:

If y=sinp xa n dy_n is the n t h derivative of y , then |[y, y_1,y_2],[y_3,y_4,y_5],[y_6,y_7,y_8]|i s (a)1 (b) 0 (c) -1 (d) none of these

(3y-3)/(y)÷(7y-7)/(3y^(2)) is

A triangle has vertices A_(i) (x_(i),y_(i)) for i= 1,2,3,. If the orthocenter of triangle is (0,0) then prove that |{:(x_(2)-x_(3),,y_(2)-y_(3),,y_(1)(y_(2)-y_(3))+x_(1)(x_(2)-x_(3))),(x_(3)-x_(1) ,,y_(3)-y_(1),,y_(2)(y_(3)-y_(1))+x_(2)(x_(3)-x_(1))),( x_(1)-x_(2),,y_(1)-y_(2),,y_(3)(y_(1)-y_(2))+x_(3)(x_(1)-x_(2))):}|=0

if (x_(1),x_(2))^(2)+(y_(1)-y_(2))^(2)=a^(2), (x_(2)-x_(3))^(2)+(y_(2)-y_(3))^(2)=b^(2) (x_(3)-x_(1))^(2)+(y_(3)-y_(1))^(2)=c^(2). where a,b,c are positive then prove that 4 |{:(x_(1),,y_(1),,1),(x_(2) ,,y_(2),,1),( x_(3),, y_(3),,1):}| = (a+b+c) (b+c-a) (c+a-b)(a+b-c)

Find the value of the polynomial f(y) =6y-3y^(2) +3 at (i) y=1 (ii) y=-1 (iii) y=0