What is the correct way to calculate the Lipschitz constant (L) for a function of two variables?

Question

Mathematics

First of all, we need to calculate the step value d for the gradient descent algorithm. It is calculated by the formula d = (1-L)/eps. The condition is the following: f(x) = x^2 + 20*(y^2 + sin(x)), x0 = 0.9, y0 = 0.7, eps = 0.9. The Lipschitz constant can be calculated using the Taylor formula:
The following are the calculations:

The final formula looks like this:
As explained to me, you need to find the sum of the maxima of the gradients in the first derivative at the point (x0,y0). How to do this specifically, I could not figure out.