[QUE/VS-06004]

Find the matrix representation of the  operator \(\frac{d}{dt}\otimes\frac{d}{ds}\) on \(P^2(t) \otimes P^2(s)\) with \(\{1, t\}\) and \(\{1,s\}\) chosen as basis  on \(P^2(t)\) and \(P^2(s)\).\[ A p(t) = p(t+1)\]  in the bases (i) \(1,t,t^2 \)  (ii)\( 1, t+t^2 , t-t^2 \)
How are the two representations related?
Here \(P^2(t)\) etc denote the space of  real polynomials in \(t\) of degree less than or equal to 2