Calculate the derivative of the function f(x,y) with respect to x by determining d/dx (f(x,y)), treating y as if it were a constant. Use the product rule and/or chain rule if necessary. For example, the first partial derivative Fx of the function f(x,y) = 3x^2*y - 2xy is 6xy - 2y.
Calculate the derivative of the function with respect to y by determining d/dy (Fx), treating x as if it were a constant. In the above example, the partial derivative Fxy of 6xy - 2y is equal to 6x - 2.
Verify that the partial derivative Fxy is correct by calculating its equivalent, Fyx, taking the derivatives in the opposite order (d/dy first, then d/dx). In the above example, the derivative d/dy of the function f(x,y) = 3x^2*y - 2xy is 3x^2 - 2x. The derivative d/dx of 3x^2 - 2x is 6x - 2, so the partial derivative Fyx is identical to the partial derivative Fxy.