3.4 Partial derivative

$y = f(x_1, x_2, x_3, \dots, x_n)$

$\frac{\partial y}{\partial x_1} = \frac{\partial f}{\partial x_1} \equiv \lim\limits_{h \to 0} \frac{f(x_1 + h, x_2, x_3, \dots, x_n) - f(x_1, x_2, \dots, x_n)}{h}$

$\frac{\partial y}{\partial x_k} = \frac{\partial f}{\partial x_k} \equiv \lim\limits_{h \to 0} \frac{f(x_1, x_2, \dots, x_k + h, \dots, x_n) - f(x_1, x_2, \dots, x_k, \dots, x_n)}{h}$