Partial Derivative

Partial Function

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

Partial Derivative

将不导的看作常数
需要在指定点有意义

Geometrically

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

Approximation 全微分

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