Gradient Vector
[Derivative](https://texonom.com/derivative-67f45809e7a84277be4fca74a3b86ceb) [Partial Derivative](https://texonom.com/partial-derivative-e9c7ff432f1c43af8669ef0addd78cd9) 


$$\vec{z}, \vec{x} \text{ } is \text{ } \text{ on the surface } f(\vec{x}) = 0$$
$$\vec{z} = \vec{x} + \epsilon\vec{u} $$
$$f(z) = f(x + \epsilon u) - f(x_1 + \epsilon u_1, x_2 + \epsilon u_2, x_3 + \epsilon u_3)$$

$$h(x, y, z) = 0$$
$$\nabla h = (\frac{dh}{dx}, \frac{dh}{dy}, \frac{dh}{dz})$$
심플하게 편미분으로 구해도 되고
$$\nabla h = \frac{d\vec{h}}{dx} \times \frac{d\vec{h}}{dy}$$
xy 아니더라도 곡면의 해당 접평면상에서 움직이는 거라 yz나 xz 도 가능


> [Untitled](https://www.cs.ucr.edu/~craigs/courses/2022-fall-cs-130/lectures/normals.pdf)






