If x=at³ and y=bt² , where t is parameter then prove that d³y / dx³=8b / 27a⁷t²

No, question is absolutely right and is of arihant.And what are u talking about continuity and differentiablity??????

dx/dt=3at² dy/dt=2bt

dy/dx=2b/3at

d²y/dx²=-2b/3at²*dt/dx=-2b/3at²*1/3at²=-2b/9a²t⁴

d³y/dx³=8b/9a²t⁵*dt/dx=8b/9a²t^5*1/3at²=8b/27a³t⁷ans

though u say its a⁷t²

I am also getting the same as u, in my view the answer of book is wrong