Statistical question of calculating 2-d distribution from distributions of the first derivative for the x and y directions

R

Hi, I do appreciate if anyone can share me an idea for solving the following problem.

I have two matrices. One for the distribution along x axis (W_x(x,y)) and one for distribution along y axis (W_y(x,y)).

The question is how to calculate a 2-d distribution from distributions of the first derivative for the x and y directions W_x(x,y) and W_y(x,y)?

thanks a lot
:-)

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