Question

what will be derivative of x=cos2x+2cosx y=sin2x-2sinx find dy/dx without evaluating

Answer 1

I think your question is x = cos2m + 2cosm and y = sin2m - 2sinm , find dy/dx

x = cos2m + 2cosm   differentiating both sides wrt x

1 = (-2sin2m - 2sinm ) dm/dx           ...........(1)

y = sin2m - 2sinm    differentiating wrt y

1 = (2cos2m - 2cosm ) dm / dy             .............(2)



dividing 2 by 1 gives  

1 =  (2cos2m - 2cosm ) dx / (-2sin2m - 2sinm) dy

dy/dx =  cos2m - cosm / -sin2m-sinm    =   - (cos2m-cosm) / sin2m + sinm

 
hope my answer is correct.