Question: How to differentiate this?

diff(F(x,F(x)), x);


how to differentiate this?


(D[1](F))(x, F(x))+(D[2](F))(x, F(x))*(diff(F(x), x))


how to find (D[1](F))(x, F(x)) and (D[2](F))(x, F(x)) ?


i guess need define new calculus for two variables

Limit((F(x+h,F(x+h)) - F(x,F(x)))/h, h = 0);

Limit((F(x+h,F(x)) - F(x,F(x)))/h, h = 0);
Limit((F(x,F(x+h)) - F(x,F(x)))/h, h = 0);

Limit((F(x+h,F(x,y)) - F(x,F(x,y)))/h, h = 0);
Limit((F(x,F(x+h,y)) - F(x,F(x,y)))/h, h = 0);


if inside F(x) is F(x,y)

it seems need to find the basic definition of F(x,y) first

if i define F(x,y) as

F := (x,y) -> min(x,y)/max(x,y);


i may be wrong, how to differentiate correctly?

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