If f(x,y) becomes g(r,t) in a transformation from Cartesian to Polar cooardinates, show that

i)

ii)

I know the partials of x and y with respect to r and t and vice-versa; I just can't get my head around how to approach the question.

I know how to find and with the chain rule, and same for g, but not the other way round. Help!