A market consists of two companies producing heterogeneous products and participating in Bertrand competition. Demand and cost functions for company 1 are

?q1?(p1?,p2?)=2??p1?+p2?? and ?C1?(q1?)=q12??

where ? > 0, while demand and cost functions for company 2 are given by

?q2?(p1?,p2?)=2?2p2?+p1?? and ?C2?(q2?)=q22??

Question

How can I inferred FOC for each company and show in detail that the best response functions are provided by

1 + 20 + 1+20 Pi(P2) 2 P210 + 5p1 P2(P1 12