Question

how do you find the partial derivative of a function with chain rule and substitution?

Answer 1

Maybe you mean this:
F=e^(x^2 +Y^2) , so set u=x^2 + y^2 du/dx=2x du/dy=2y
fx=e^u * du/dx = e^(x^2 + y^2) * 2x same process for fy.