| dz/dt=2tf_x(t^2,t^3)+(3t^2)f_y(t^2,t^3) を使って積の微分を適用します。
(d^2/dt^2)z=2f_x(t^2,t^3)+2t(d/dt)f_x(t^2,t^3) +6tf_y(t^2,t^3)+(3t^2)(d/dt)f_y(t^2,t^3) =2f_x(t^2,t^3)+2t{2tf_xx(t^2,t^3)+(3t^2)f_xy(t^2,t^3)} +6tf_y(t^2,t^3)+(3t^2){2tf_yx(t^2,t^3)+(3t^2)f_yy(t^2,t^3)} =2f_x(t^2,t^3)+6tf_y(t^2,t^3) +(4t^2)f_xx(t^2,t^3)+(12t^3)f_xy(t^2,t^3)+(9t^4)f_yy(t^2,t^3) ∴ (d^2/dt^2)z|[t=1]=2f_x(1,1)+6f_y(1,1)+4f_xx(1,1)+12f_xy(1,1)+9f_yy(1,1)
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