Undergraduate

What is the differential of surface area, dS , in space? If f and its first partial derivatives are continuous on the closed region R

What is the differential of surface area, dS, in space?
If f and its first partial derivatives are continuous on the closed region R in the xy-plane, then the differential of the surface area given by
z = f(x, y) over R
is which of the following?
dS =
[fy(x, y)]2
dy
dS =
1+[fx(x, y)]2+[fy(x, y)]2
dA
dS =
[fx(x, y)]2+[fy(x, y)]2
dA
dS =
1+[fy(x, y)]2
dy
dS =
[f(x)]2
dx
dS =
1+[f(x)]2
dx

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