Search for question

and suppose that \frac{\partial f}{\partial z} \frac{\partial g}{\partial w}-\frac{\partial f}{\partial w} \frac{\partial g}{\partial z} \neq 0 Show that \left(\frac{\partial z}{d x}\right)_{y}=-\frac{\frac{\partial f}{\partial x} \frac{\partial g}{\partial v}-\frac{\partial f}{\partial w} \frac{\partial g}{\partial x}}{\frac{\partial f}{\partial z} \frac{\partial g}{\partial h}-\frac{\partial f}{\partial h v} \frac{\partial g}{d z}} and \left(\frac{\partial w}{\partial y}\right)_{\bar{x}}=-\frac{\frac{\partial f}{d z} \frac{\partial g}{\partial y}-\frac{\partial f}{\partial y} \frac{\partial g}{d z}}{\frac{\partial f}{\partial z} \frac{\partial g}{\partial w}-\frac{\partial f}{\partial w} \frac{\partial g}{\partial z_{z}}} .

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5

Fig: 6