Give an appropriate answer.How are the partial derivatives ?f/?x and ?f/?y of a function f(x,y) defined? How are they interpreted and calculated?

Question

What will be an ideal response?

Answer 1

Definitions:
 (a, b) =    and  (a, b) =   

?f/?x is the slope of the line tangent at (a,b) to the cross-section curve z = f(x, b).
 ?f/?y is the slope of the line tangent at (a,b) to the cross-section curve z = f(a, y).

?f/?x is calculated by treating y as a constant and then applying the standard rules for differentiation of a function with respect to x.
?f/?y is calculated by treating x as a constant and then applying the standard rules for differentiation of a function with respect to y.