Question

3.已知 e^z-sinxyz=xy 求(z)/(x) , (z)/(y)

Answer 1

问：3.已知 e^z-sinxyz=xy 求(z)/(x) , (z)/(y)

答：对于已知方程 $e^z - \sin(xy)z = xy$，要求 $\frac{z}{x}$ 和 $\frac{z}{y}$，可以利用偏导数的概念来求解。首先对方程两边同时求偏导数，得到：$\frac{\partial}{\partial x}(e^z - \sin(xy)z) = y$$\frac{\partial}{\partial y}(e^z - \sin(xy)z) = x$因此：$\frac{\partial z}{\partial x}e^z - z\cos(xy)\frac{\partial (xy)}{\partial x} = y$$\frac{\partial z}{\partial y}e^z - z\cos(xy)\frac{\partial (xy)}{\partial y} = x$化简原式，得到：$\frac{z}{x} = \frac{ye^z}{e^z - zy\cos(xy)}$$\frac{z}{y} = \frac{xe^z}{e^z - zx\cos(xy)}$因此，$\frac{z}{x} = \fr

答：亲，特殊符号显示不出来，接下去以图文形式发送给你