Find Sf/Sx and Sf/Sy for f=1/2x-3y

Question

Calculus 3: Functions of two Variables involving limits if i am not mistaken. It has to be solved using these two formulas.

1: Sf/Sx=fx(x,y)=lim f(x+Sx,y)-f(x,y) then the whole thing divide by Sy.

                         x→0

2: Sf/Sy=fy(x,y)=lim  f(x,y+Sy)-f(x,y) then the whole thing divide by Sy.

                          x→0

Answer 1

f(x,y) = (2x-3y)^-1

 

To find the partial derivative of f with respect to x, treat y as a constant and differentiate with respect to x:

 

∂f/∂x = -(2x-3y)^-2(2) = -2/(2x-3y)²

 

To find the partial derivative of f with respect to y, treat x as a constant and differentiate with respect to y:

 

∂f/∂y = -(2x-3y)^-2(-3) = 3/(2x-3y)²