2xe^y - πe = tlnt ,两边对 t 求导,得 2e^y(dx/dt) + 2xe^y(dy/dt) = 1+lnt ;
ysinx = t + lnt , 两边对 t 求导,得 ycosx(dx/dt) + sinx(dy/dt) = 1+1/t.
联立解得 dx/dt = [sinx(1+lnt)-2xe^y(1+1/t)]/[2e^y(sinx-xycosx)]
dy/dt = [2e^y(1+1/t)-ycosx(1+lnt)]/[2e^y(sinx-xycosx)]
dy/dx = (dy/dt)/(dx/dt) = [2e^y(1+1/t)-ycosx(1+lnt)]/[sinx(1+lnt)-2xe^y(1+1/t)]
x = π/2, y = 1, t = 1 时,dy/dx = 4e/(1-πe)。