Then h(x, y) has a continuous partial derivative with respect to d, while in? The constant on d is equal to 0.

H(x, y) is continuous, D is a bounded closed region, and h(x, y) can get the maximum and minimum values on D. 。

What about the maximum and minimum values? D, that is, the maximum and minimum values of h(x, y) are both 0.

H(x, y) is a constant equal to 0, and f (x, y) = g (x, y) holds for any (x, y) ∈ D 。

So ▽f(x, y) = ▽g(x, y) is also true for any (x, y) ∈ D, and naturally it is also true for (x, y) ∈ d 0.

What if the maximum and minimum values are not there? D, let h(x, y) take the maximum or minimum value at (x0, y0) ∈ d 0.

Then ▽ f (x0, y0)-▽ g (x0, y0) = ▽ h (x0, y0) = 0.

That is, (x0, y0) ∈ d 0 exists, so ▽f(x0, y0) = ▽g(x0, y0).