📝 题目
5.3.4 求由下列方程所确定的 $z = z\left( {x,y}\right)$ 的微分:
(1) $f\left( {{xy},z - y}\right) = 0$ ; (2) $f\left( {x,x + y,x + y + z}\right) = 0$ .
💡 答案与解析
5.3.4 (1) $\mathrm{d}z = - \frac{y{f}_{1}^{\prime }}{{f}_{2}^{\prime }}\mathrm{d}x + \frac{{f}_{2}^{\prime } - x{f}_{1}^{\prime }}{{f}_{2}^{\prime }}\mathrm{d}y$ ;
(2) $\mathrm{d}z = - \frac{{f}_{1}^{\prime } + {f}_{2}^{\prime } + {f}_{3}^{\prime }}{{f}_{3}^{\prime }}\mathrm{d}x - \frac{{f}_{2}^{\prime } + {f}_{3}^{\prime }}{{f}_{3}^{\prime }}\mathrm{d}y$ .