If `y=u/v` then `dy/dx=?`

If y = f(u) is a differentiable functions of u and u = g(x) is a differentiable functions of x such that the composite functions y = f[g(x) ] is a differentiable functions of x then (dy)/(dx) = (dy)/(du) . (du)/(dx) Hence find (dy)/(dx) if y = sin ^(2)x

If y=sqrt(u) ,u=(3-2v)v and v=x^(2) , then (dy)/(dx)=

If y=(1)/(4)u^(4),u=(2)/(3)x^(3)+5 , then (dy)/(dx)=

If : (dx)/(dy)=u" and "(d^(2)x)/(dy^(2))=v," then: "(d^(2)y)/(dx^(2))=

If x=sqrt (1+u^(2)),y =log (1+u^(2) ) ,then (dy)/(dx) =

If y=x^(2)+1" and "u=sqrt(1+x^(2))," then: "(dy)/(dx)=

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

If y = (u -1)/(u + 1) and u = sqrt(x) , then (dy)/(dx) is

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 = sin x^(@) " and " u = cos x " then " (dy)/(dx) is equal to