f(x, y) is a function of two variables x and y that we wish to change to variables s and t, where s x 2 y 2 , t xy Determine fxx and fyy in terms of s, t, f s , f t , f ss , f tt and f st Show that fxx fyy (s 4t)(4ss f1)

Question: f(x, y) is a function of two variables x and y that we wish to change to variables s and t, where s = x

f(x, y) is a function of two variables x and y that we wish to change to variables s and t, where s = x² – y², t = xy. Determine fxx and fyy in terms of s, t, f_s, f_t, f_ss, f_tt and f_st. Show that

fxx + fyy= (s + 41) (4fss+ft1)

fxx + fyy = (s + 4t)(4ss +f1)

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