Is it right... To say.... dy/dx = dx/dy

No this is incorrect.

(dy/dx) is actually equal to (dx/dy)^-1

dy/dx=1/(dx/dy)

No,dy/dx=1/(dx/dy)

i dont know

acctualy dy/dx=1/dx/dy

no

never

dy\dx is change of y w.r.t x

but dx\dy is change of x w.r.t y which will turn out to be inverse of each other