If `y=(u)/(v)`, where u and v are functions of x, show that
`v^(3)(d^(2)y)/(dx^(2))=|{:(u,v,0),(u',v,v),(u'',v'',2v'):}|`.

If y=u//v," where "u,v," are differentiable functions of x and "vne0," then: "u(dv)/(dx)+v^(2)(dy)/(dx)=

If u,v and w are functions of x ,then show that (d)/(dx)(u*v*w)=(du)/(dx)v*w+u*(dv)/(dx)*w+u*v(dw)/(dx) in two ways - first by repeated application of product rule,second by logarithmic differentiation.

If (x+iy)^(3)=u+iv, then show that (u)/(x)+(v)/(y)=4(x^(2)-y^(2))

If (x+iy)^(3)=u+iv then show that (u)/(x)+(v)/(y)=4(x^(2)-y^(2))

If u=inte^(ax)sin " bx dx" and v=inte^(ax)cos " bx dx then "(u^(2)+v^(2))(a^(2)+b^(2))=

Prove that d/(dx)|(u_1,v_1,w_1),(u_2,v_2,w_2),(u_3,v_3,w_3)|=|(u_1,v_1,w_1),(u_2,v_2,w_2),(u_4,v_4,w_4)| where u,v,w are functions of x and (du)/(dx)=u_1,(d^2u)/(dx^2)=u_2, etc.

int_(1)^(2)((x^(2)-1)dx)/(x^(3)*sqrt(2x^(4)-2x^(2)+1))=(u)/(v) where u are ( in their blowest form.Find the value of )/(sqrt(2x^(4)-2x^(2)+1))=(u)/(v) where of ((1000)u)/(v)

If (x,y) and (x,y) are the coordinates of the same point referred to two sets of rectangular axes with the same origin and it ux+vx+vy , where u and v are independent of x and y becomes VX+UY, show that u^(2)+v^(2)=U^(2)+V^(2)