the concept of partial derivatives goes like this. when you have a multivariable function and you want to find the partial derivative with respect to one of those variables, you treat all the other variables as constants and find the derivative of the desired variable normally.

F(x,y) = sin(xy)

dF/dy = xcos(xy) ........i do the chain rule treating x as a number. if x is a number, the derivative of xy is x, so i multiply by x to satisfy the chain rule

dF/dx = ycos(xy)

now plug in your values

note, these are partial derivatives, so the d's should be written like lower case delta's