$$-gydF4y2Ba\nabla gydF4y2Ba\cdot gydF4y2Ba(gydF4y2Ba\mathrm{cgydF4y2Ba}\nabla gydF4y2Ba\mathrm{ugydF4y2Ba})gydF4y2Ba+gydF4y2Ba\mathrm{一个gydF4y2Ba}\mathrm{ugydF4y2Ba}=gydF4y2Ba\mathrm{fgydF4y2Ba}$$

$$(gydF4y2Ba\mathrm{1gydF4y2Ba}+gydF4y2Ba{\mathrm{xgydF4y2Ba}}^{\mathrm{2gydF4y2Ba}})gydF4y2Ba\frac{{\partial gydF4y2Ba}^{\mathrm{2gydF4y2Ba}}\mathrm{ugydF4y2Ba}}{\partial gydF4y2Ba{\mathrm{xgydF4y2Ba}}^{\mathrm{2gydF4y2Ba}}}-gydF4y2Ba\mathrm{3gydF4y2Ba}\mathrm{xgydF4y2Ba}\mathrm{ygydF4y2Ba}\frac{{\partial gydF4y2Ba}^{\mathrm{2gydF4y2Ba}}\mathrm{ugydF4y2Ba}}{\partial gydF4y2Ba\mathrm{xgydF4y2Ba}\partial gydF4y2Ba\mathrm{ygydF4y2Ba}}+gydF4y2Ba\frac{(gydF4y2Ba\mathrm{1gydF4y2Ba}+gydF4y2Ba{\mathrm{ygydF4y2Ba}}^{\mathrm{2gydF4y2Ba}})gydF4y2Ba}{\mathrm{2gydF4y2Ba}}\frac{{\partial gydF4y2Ba}^{\mathrm{2gydF4y2Ba}}\mathrm{ugydF4y2Ba}}{\partial gydF4y2Ba{\mathrm{ygydF4y2Ba}}^{\mathrm{2gydF4y2Ba}}}=gydF4y2Ba\mathrm{0gydF4y2Ba}$$

$$\mathrm{cgydF4y2Ba}=gydF4y2Ba(gydF4y2Ba\begin{array}{cc}{\mathrm{cgydF4y2Ba}}_{\mathrm{1gydF4y2Ba}}& {\mathrm{cgydF4y2Ba}}_{\mathrm{3gydF4y2Ba}}\\ {\mathrm{cgydF4y2Ba}}_{\mathrm{2gydF4y2Ba}}& {\mathrm{cgydF4y2Ba}}_{\mathrm{4gydF4y2Ba}}\end{array})gydF4y2Ba$$

$$\begin{array}{c}\nabla gydF4y2Ba·gydF4y2Ba(gydF4y2Ba\mathrm{cgydF4y2Ba}\nabla gydF4y2Ba\mathrm{ugydF4y2Ba})gydF4y2Ba=gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{1gydF4y2Ba}}{\mathrm{ugydF4y2Ba}}_{\mathrm{xgydF4y2Ba}\mathrm{xgydF4y2Ba}}+gydF4y2Ba(gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{2gydF4y2Ba}}+gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{3gydF4y2Ba}})gydF4y2Ba{\mathrm{ugydF4y2Ba}}_{\mathrm{xgydF4y2Ba}\mathrm{ygydF4y2Ba}}+gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{4gydF4y2Ba}}{\mathrm{ugydF4y2Ba}}_{\mathrm{ygydF4y2Ba}\mathrm{ygydF4y2Ba}}\\ +gydF4y2Ba(gydF4y2Ba\frac{\partial gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{1gydF4y2Ba}}}{\partial gydF4y2Ba\mathrm{xgydF4y2Ba}}+gydF4y2Ba\frac{\partial gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{2gydF4y2Ba}}}{\partial gydF4y2Ba\mathrm{ygydF4y2Ba}})gydF4y2Ba{\mathrm{ugydF4y2Ba}}_{\mathrm{xgydF4y2Ba}}+gydF4y2Ba(gydF4y2Ba\frac{\partial gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{3gydF4y2Ba}}}{\partial gydF4y2Ba\mathrm{xgydF4y2Ba}}+gydF4y2Ba\frac{\partial gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{4gydF4y2Ba}}}{\partial gydF4y2Ba\mathrm{ygydF4y2Ba}})gydF4y2Ba{\mathrm{ugydF4y2Ba}}_{\mathrm{ygydF4y2Ba}}\end{array}$$

$$\begin{array}{l}{\mathrm{cgydF4y2Ba}}_{\mathrm{1gydF4y2Ba}}=gydF4y2Ba-gydF4y2Ba(gydF4y2Ba\mathrm{1gydF4y2Ba}+gydF4y2Ba{\mathrm{xgydF4y2Ba}}^{\mathrm{2gydF4y2Ba}})gydF4y2Ba\\ {\mathrm{cgydF4y2Ba}}_{\mathrm{4gydF4y2Ba}}=gydF4y2Ba-gydF4y2Ba(gydF4y2Ba\mathrm{1gydF4y2Ba}+gydF4y2Ba{\mathrm{ygydF4y2Ba}}^{\mathrm{2gydF4y2Ba}})gydF4y2Ba/gydF4y2Ba\mathrm{2gydF4y2Ba}\end{array}$$

$$\begin{array}{l}(gydF4y2Ba\frac{\partial gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{1gydF4y2Ba}}}{\partial gydF4y2Ba\mathrm{xgydF4y2Ba}}+gydF4y2Ba\frac{\partial gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{2gydF4y2Ba}}}{\partial gydF4y2Ba\mathrm{ygydF4y2Ba}})gydF4y2Ba=gydF4y2Ba-gydF4y2Ba\mathrm{2gydF4y2Ba}\mathrm{xgydF4y2Ba}+gydF4y2Ba\frac{\partial gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{2gydF4y2Ba}}}{\partial gydF4y2Ba\mathrm{ygydF4y2Ba}}\\ \text{所以gydF4y2Ba}\\ {\mathrm{cgydF4y2Ba}}_{\mathrm{2gydF4y2Ba}}=gydF4y2Ba\mathrm{2gydF4y2Ba}\mathrm{xgydF4y2Ba}\mathrm{ygydF4y2Ba}。gydF4y2Ba\\ (gydF4y2Ba\frac{\partial gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{3gydF4y2Ba}}}{\partial gydF4y2Ba\mathrm{xgydF4y2Ba}}+gydF4y2Ba\frac{\partial gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{4gydF4y2Ba}}}{\partial gydF4y2Ba\mathrm{ygydF4y2Ba}})gydF4y2Ba=gydF4y2Ba\frac{\partial gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{3gydF4y2Ba}}}{\partial gydF4y2Ba\mathrm{xgydF4y2Ba}}-gydF4y2Ba\mathrm{ygydF4y2Ba}\\ \text{所以gydF4y2Ba}\\ {\mathrm{cgydF4y2Ba}}_{\mathrm{3gydF4y2Ba}}=gydF4y2Ba\mathrm{xgydF4y2Ba}\mathrm{ygydF4y2Ba}\end{array}$$

$$-gydF4y2Ba\nabla gydF4y2Ba\cdot gydF4y2Ba(gydF4y2Ba\mathrm{cgydF4y2Ba}\nabla gydF4y2Ba\mathrm{ugydF4y2Ba})gydF4y2Ba=gydF4y2Ba\mathrm{0gydF4y2Ba}$$

$$\stackrel{\to gydF4y2Ba}{\mathrm{ngydF4y2Ba}}·gydF4y2Ba(gydF4y2Ba\mathrm{cgydF4y2Ba}\nabla gydF4y2Ba\mathrm{ugydF4y2Ba})gydF4y2Ba+gydF4y2Ba\mathrm{问gydF4y2Ba}\mathrm{ugydF4y2Ba}=gydF4y2Ba\mathrm{ggydF4y2Ba}$$

$$\begin{array}{c}\nabla gydF4y2Ba·gydF4y2Ba(gydF4y2Ba\mathrm{cgydF4y2Ba}\nabla gydF4y2Ba\mathrm{ugydF4y2Ba})gydF4y2Ba=gydF4y2Ba\nabla gydF4y2Ba·gydF4y2Ba(gydF4y2Ba(gydF4y2Ba\begin{array}{cc}{\mathrm{cgydF4y2Ba}}_{\mathrm{1gydF4y2Ba}}& {\mathrm{cgydF4y2Ba}}_{\mathrm{3gydF4y2Ba}}\\ {\mathrm{cgydF4y2Ba}}_{\mathrm{2gydF4y2Ba}}& {\mathrm{cgydF4y2Ba}}_{\mathrm{4gydF4y2Ba}}\end{array})gydF4y2Ba(gydF4y2Ba\begin{array}{c}{\mathrm{ugydF4y2Ba}}_{\mathrm{xgydF4y2Ba}}\\ {\mathrm{ugydF4y2Ba}}_{\mathrm{ygydF4y2Ba}}\end{array})gydF4y2Ba)gydF4y2Ba\\ =gydF4y2Ba\frac{\partial gydF4y2Ba}{\partial gydF4y2Ba\mathrm{xgydF4y2Ba}}(gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{1gydF4y2Ba}}{\mathrm{ugydF4y2Ba}}_{\mathrm{xgydF4y2Ba}}+gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{3gydF4y2Ba}}{\mathrm{ugydF4y2Ba}}_{\mathrm{ygydF4y2Ba}})gydF4y2Ba+gydF4y2Ba\frac{\partial gydF4y2Ba}{\partial gydF4y2Ba\mathrm{ygydF4y2Ba}}(gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{2gydF4y2Ba}}{\mathrm{ugydF4y2Ba}}_{\mathrm{xgydF4y2Ba}}+gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{4gydF4y2Ba}}{\mathrm{ugydF4y2Ba}}_{\mathrm{ygydF4y2Ba}})gydF4y2Ba\\ =gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{1gydF4y2Ba}}{\mathrm{ugydF4y2Ba}}_{\mathrm{xgydF4y2Ba}\mathrm{xgydF4y2Ba}}+gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{4gydF4y2Ba}}{\mathrm{ugydF4y2Ba}}_{\mathrm{ygydF4y2Ba}\mathrm{ygydF4y2Ba}}+gydF4y2Ba(gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{2gydF4y2Ba}}+gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{3gydF4y2Ba}})gydF4y2Ba{\mathrm{ugydF4y2Ba}}_{\mathrm{xgydF4y2Ba}\mathrm{ygydF4y2Ba}}\end{array}$$

$$\stackrel{\to gydF4y2Ba}{\mathrm{ngydF4y2Ba}}·gydF4y2Ba(gydF4y2Ba\mathrm{cgydF4y2Ba}\nabla gydF4y2Ba\mathrm{ugydF4y2Ba})gydF4y2Ba=gydF4y2Ba\mathrm{2gydF4y2Ba}$$

$$-gydF4y2Ba\nabla gydF4y2Ba\cdot gydF4y2Ba(gydF4y2Ba\mathrm{cgydF4y2Ba}\nabla gydF4y2Ba\mathrm{ugydF4y2Ba})gydF4y2Ba+gydF4y2Ba\mathrm{一个gydF4y2Ba}\mathrm{ugydF4y2Ba}=gydF4y2Ba\mathrm{fgydF4y2Ba}$$

$$\frac{{\partial gydF4y2Ba}^{\mathrm{2gydF4y2Ba}}\mathrm{ugydF4y2Ba}}{\partial gydF4y2Ba{\mathrm{xgydF4y2Ba}}^{\mathrm{2gydF4y2Ba}}}+gydF4y2Ba\frac{\mathrm{因为gydF4y2Ba}(gydF4y2Ba\mathrm{xgydF4y2Ba}+gydF4y2Ba\mathrm{ygydF4y2Ba})gydF4y2Ba}{\mathrm{4gydF4y2Ba}}\frac{{\partial gydF4y2Ba}^{\mathrm{2gydF4y2Ba}}\mathrm{ugydF4y2Ba}}{\partial gydF4y2Ba\mathrm{xgydF4y2Ba}\partial gydF4y2Ba\mathrm{ygydF4y2Ba}}+gydF4y2Ba\frac{\mathrm{1gydF4y2Ba}}{\mathrm{2gydF4y2Ba}}\frac{{\partial gydF4y2Ba}^{\mathrm{2gydF4y2Ba}}\mathrm{ugydF4y2Ba}}{\partial gydF4y2Ba{\mathrm{ygydF4y2Ba}}^{\mathrm{2gydF4y2Ba}}}=gydF4y2Ba\mathrm{0gydF4y2Ba}$$

$$\begin{array}{c}{\mathrm{cgydF4y2Ba}}_{\mathrm{2gydF4y2Ba}}+gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{3gydF4y2Ba}}=gydF4y2Ba\frac{-gydF4y2Ba\mathrm{因为gydF4y2Ba}(gydF4y2Ba\mathrm{xgydF4y2Ba}+gydF4y2Ba\mathrm{ygydF4y2Ba})gydF4y2Ba}{\mathrm{4gydF4y2Ba}}\\ \frac{\partial gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{1gydF4y2Ba}}}{\partial gydF4y2Ba\mathrm{xgydF4y2Ba}}+gydF4y2Ba\frac{\partial gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{2gydF4y2Ba}}}{\partial gydF4y2Ba\mathrm{ygydF4y2Ba}}=gydF4y2Ba\frac{\partial gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{2gydF4y2Ba}}}{\partial gydF4y2Ba\mathrm{ygydF4y2Ba}}=gydF4y2Ba\mathrm{0gydF4y2Ba}\\ \frac{\partial gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{3gydF4y2Ba}}}{\partial gydF4y2Ba\mathrm{xgydF4y2Ba}}+gydF4y2Ba\frac{\partial gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{4gydF4y2Ba}}}{\partial gydF4y2Ba\mathrm{ygydF4y2Ba}}=gydF4y2Ba\frac{\partial gydF4y2Ba{\mathrm{cgydF4y2Ba}}_{\mathrm{3gydF4y2Ba}}}{\partial gydF4y2Ba\mathrm{xgydF4y2Ba}}=gydF4y2Ba\mathrm{0gydF4y2Ba}\end{array}$$