Partial Derivative

Apr 3, 2023

$w = f(x_0, y)$ the partial function for $x = x_0$.

将不导的看作常数
需要在指定点有意义

过一点的切平面
设 $w = f(x, y)$ 在 $(x_0, y_0)$ 处切平面方程为
$$w - w_0 = (\frac{\partial w}{\partial x})(x - x_0) + (\frac{\partial w}{\partial y})(y - y_0)$$

$$\Delta w \approx (\frac{\partial w}{\partial x})\Delta x + (\frac{\partial w}{\partial y}) \Delta y $$