Section 14.4 Chain Rules with two variables
[h(t2,t3)] = hx(t2,t3) d dt (t2) +hy(t2,t3) d dt (t3) = 2thx(t 2,t3) +3t2hy(t2,t3). Therefore, G0(2) = 2(2)hx(22,23)+ 3(22)hy(22,23) = 4hx(4,8)+ 12hy(4,8) = 4(10) + 12(−20) = −200. In applications it often helps to interpret the Chain Rule formula (1) in terms of rates of change. We write it in the form dF dt = ∂F