find dy/dx to equation y= sin (2 times square root of x divided by x-1)?

Answer 1

y = sin (2√x ) / (x - 1)
Use quotient rule:-
dy / dx is given by:-
[(x - 1) cos (2√x) (x)^(-1/2) - sin(2√x) ] / (x - 1) ²

Answer 2

Did you mean y =sin(2(√x)/(x-1))
which has dy/dx = -(x+1)cos(2(√x)/(x-1)) / ((√x)(x-1)²)

Or did you mean y = sin(2√(x/(x-1)))
which has dy/dx = - cos(2√(x/(x-1))) / ((√x)(x-1)^(3/2))